new scan Beller draws her argument from her radical new reading of the history of the quantum revolution, especially th

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Science and Its Conceptual Foundations A series edited by David 1. Hull

Quantwn

Dialogue The Making of a Revolution

Mara Beller

THE

UNIVERSITY

OF

CHICAGO

Chicago & London

PRESS

MAllA BE1..LE1t is the Barbara Druss Dibner Professor in History and Philosophy of Science at the Hebrew University of Jerusalem. The University of Chicago Press, Chicago 60637 The University of Chicago Press, Ltd., London C> 1999 by The University of Chicago All rights reserved. Published 1999 Printed in the United States of America 080706 05 04 03 02 01 00 99 12345 ISBN: 0-226-04181-6 (cloth) Photo credits: All courtesy American Institute of Physics, Emilio Segre Visual Archives. Heisenberg and Bohr, photo by Paul Ehrenfest Jr. Bohr and Einstein, photo by Paul Ehrenfest Jr. Stern, Pauli, and Heisenberg, photo by Paul Ehrenfest Jr. Dirac and Heisenberg, Physics Today Collection. Bohr, Franck, and Hansen, Margrethe Bohr Collection. schrodinger, king of Sweden, and Heisenberg, Max-Planck-Institut fUr Physik. Bohr and Pauli, CERN. Einstein and Pauli, photo by Paul Ehrenfest Jr. Zernike, W. F. Meggers Collection. Library of Congress Cataloging-in-Publication Data Beller, Mara. Quantum dialogue: the making of a revolution / Mara Beller. p. cm.-(Science and its conceptual foundations) Includes bibliographical references and index. ISBN 0-226-04181-6 (cloth: alk. paper) 1. Quantum theory. 2. Communication in physics. 3. PhysicsPhilosophy. I. Title. II. Series. QCI74.13.B45 1999 530. 12-dc21

99-35499 CIP

@) The paper used in this publication meets the minimum requirements of the American National Standard for Information Sciences-Permanence of Paper for Printed Library Materials, ANSI Z39.48-1992.

In memory of my mother.

Ida Baruch

Thinking and discourse are the same thing. ... What we call thinking is precisely the inward dialogue. Plato

The roads by which men arrive at their insights . .. seem to me almost as worthy of wonder as these matters in themselves. Johannes Kepler

Revolutions are true as movements and false as regimes. Maurice Merleau-Ponty

CONTENTS ~

List of lllustrations Preface and Acknowledgments

1.

xiii

Novelty and Dogma Dialogical Creativity Rhetorical Strategies

PART ONE

2.

xi 1

1 10

DIALOGICAL EMERGENCE

Matrix Theory in Flux

17

Introduction 17 18 A Revision of the Origins of the Matrix Theory The Emotional Confrontation between the Matrix 30 Physicists and Schrodinger Born's Probabilistic Interpretation: A Case Study of "Concepts in Flux" 39

3.

Quantum Philosophy in Flux

51

Introduction 51 Positivism in Flux 52 Indeterminism in Flux 59

4.

The Dialogical Emergence of Heisenberg's Uncertainty Paper Introduction 65 Dialogue with SchrOdinger 67 79 Dialogue with Pauli Dialogue with Dirac 85 91 Dialogue with Jordan Dialogues with "Lesser" Scientists

96

65

viii

5.

Contents

The Polyphony of Heisenberg's Uncertainty Paper Introduction 103 The Polyphony of the Notion of Interpretation The Contingency of Acausality 110 Anschaulichkeit and the Status of Oassical Concepts 113

6.

103

106

The Dialogical Birth of Bohr's Complementarity

117

Introduction 117 Dialogue with Schrodinger: The Structure of Atoms 122 Dialogue with Einstein and Compton 131 Dialogue with Campbell 135 Clash with Heisenberg: Setting the Historical Record Straight 138 Confrontation with Pauli 141 Conclusion 143

7.

The Challenge of Einstein-Podolsky-Rosen and the Two Voices of Bohr's Response

145

Two Voices in Bohr's Response to Einstein-PodolskyRosen 145 Bohr's Victory? 151 Disturbance, Reality, and Acausality 155 Bohr's Doctrine of the Indispensability of Oassical Concepts and the Correspondence Principle 160 PART Two

8.

RHETORICAL CONSOLIDATION

The Polyphony of the Copenhagen Interpretation and the Rhetoric of Antirealism Introduction 171 What Scientists "Need Not" and "Must Not" Do 173 The Appeal of Antirealism: Some General Considerations 176 Reality, Oassical Concepts, and Symbols 179 The Appeal of Antirealism: Bohr's Version 184 Antirealism and Opposition 185 The Appearance of Consensus and Conclusion 187

171

Contents

9.

The Copenhagen Dogma: The Rhetoric of Finality and Inevitability

ix

191

Introduction 191 Acausality and the Indispensability of Oassical Concepts 194 Operationalism: From Consistency to Inevitability Arguments 199 Bohm on Classical versus Quantum Concepts and on Indeterminism 206

10.

Constructing the Orthodox Narrative

211

Introduction: ''Whiggish'' History and "Winner's" Strategies 211 Discontinuities and Quantum Jumps 214 Indeterminism and Historiographical Doubts 220

11.

The Myth of Wave-Particle Complementarity

223

Introduction: The Dramatic Historical Narrative 223 Mathematical Physicists and the Wave-Particle Dilemma 227 Ambiguity and the Wave-Particle Issue 232 Ideological and Pedagogical Uses of Wave-Particle Complementarity 237

12.

Complementarity as Metaphor

243

Introduction 243 The Web of Correspondences and Harmonies 248 "Wholeness" as Metaphor 252 Bohr: Mathematics and Common Language 259 Metaphorical Appeal and Conclusion 262

13.

Hero Worship, Construction of Paradigms, and Opposition Introduction 269 Bohr and Hero Worship 270 The Issue of Consistency 275 Opposition, Paradigms, and Past Science

14.

269

276

Dialogues or Paradigms? Introduction 287 Heisenberg's /lOosed Theories" and Kuhnian "Paradigms" 288 Where Did Kuhnian Incommensurability Come From? 290

287

x

Contents

Hanson's Incommensurability and the Copenhagen Dogma 294 Paradigms and the History of Science 300 Paradigms and Holism 302 Paradigms and Creativity 304

15.

Dialogical Philosophy and Historiography: A Tentative Outline

307

In Praise of Disagreement 308 The Philosophical and Historiographical Advantages of DiaJogism 313 Theory as Practice: Between Tools and Metaphors 317 Truth and Beauty 320

References Index

327 355

ILL USTRATIONS ~

Diagrams 72 Heisenberg's analysis of a y-ray microscope Bohr's thought experiments in terms of classical concepts

148

Photographs (following page 190) Werner Heisenberg and Niels Bohr Niels Bohr and Albert Einstein Otto Stern, Wolfgang Pauli, and Werner Heisenberg Paul Dirac and Werner Heisenberg Niels Bohr, James Franck, and Hans Hansen Erwin Schrodinger, the king of Sweden, and Werner Heisenberg Walther Meissner, Max Born, and James Franck Niels Bohr and Wolfgang Pauli Albert Einstein and Wolfgang Pauli Frits Zemike William Duane Niels Bohr, Wolfgang Pauli, Lothar Nordheim, and Leon Rosenfeld

PREFACE AND ACKNOWLEDGMENTS 1:::;::1

This book is about scientific dialogues that made the quantum revolution. The description of the intricate flux of these dialogues reveals the dynamic and intensely personal nature of scientific theorizing. During the work on this book I came to the rewarding realization that an ongoing responsiveness to the concerns of others, in addition to being a basic human value, is a precondition of scientific creativity. This book deals with the anatomy of scientific discovery (part 1) and with the strategies of consolidation of the orthodox quantum philosophy (part 2). My approach is based on both admiration for the creation of scientific novelty and criticism toward the establishment of scientific dogmas. This book offers a thorough historical reevaluation of the emergence and consolidation of the Copenhagen interpretation of quantum physics-the dominant interpretation since its launching in 1927 by Niels Bohr, Werner Heisenberg, and Max Born. It is not a historian's task to offer a specific alternative to the orthodox Copenhagen interpretation. I take no stand on the existing alternatives to the orthodox philosophy. This book does not deal with the extensive and lively contemporary research on the philosophical problems of quantum physiCS. Rather, my historical, philosophical, and sociological analysis of the Copenhagen philosophy demonstrates the possibility and the need of a viable alternative to the orthodox interpretation. As my work on this book progressed, my revision of the history of the quantum revolution gradually evolved into a general critique of the revolutionary narratives for the description of the scientific change. Focusing on the quantum revolution, this book provides an analysis of how revolutionary stories in history of science are constructed, how division between "winners" and "losers" is fabricated, how the opposition is misrepresented and delegitimized, and how the illusion of the existence of a paradigmatic consensus among participants is achieved.

xiv

Preface and Acknowledgments

The bulk of my critical analysis of the Copenhagen philosophy of complementarity and indeterminism is found in part 2, which is more accessible to the general reader and can be read separately from the rest of the book. Nevertheless, parts 1 and 2 are mutually illuminating and conceptually interconnected. The introductory chapter 1 offers an overview of the major themes of this book, while the concluding chapter 15 is an argument for the dialogical approach for studying the advance of scientific knowledge. This book was long in the making, and I have accumulated a long list of debts. There are a few scholars to whom my debt and gratitude are especially deep. Many ideas in this book were developed while I imagined addressing Arthur Fine. Arthur's writings and personal encouragement were invaluable. lowe a great debt to Jim Cushing, for his unbelievably meticulous and caring reading of the draft of this book, for his continuous support, and for his important work on related issues. Yemima Ben-Menahem, a colleague and friend, provided valuable criticism with a rare combination of philosophical wisdom and graceful encouragement. Sam Schweber and John Stachel, who took an early interest in my work, were always very generous with their intellectual and personal support. Tom Ryckman attentively read the draft of this book and provided valuable comments. I am grateful to Allan Franklin for many stimulating and pleasant conversations we had during my stay in Boulder. I am fortunate to have a friendly and stimulating environment, with Yehuda Elkana, a teacher and a founder of an extensive academic activity in history and philosophy of science in Israel, and with colleagues at The Hebrew University of Jerusalem such as Yaron Ezrahi, Rafi Falk, Michael Head, ltamar Pitowsky, Mark Steiner, and !sachar Unna. My list of debts is a long one, from Stephen Brush, my Ph.D. adviser in the early days of my academic life, to Shelly Goldstein and Anna Sfard, with whom I recently engaged in fruitful dialogues. I am also grateful to the following people for their stimulation, support, or assistance at some stage of working on this project: Pnina Abir-Am, Gideon Akavia, Diana Barkan, the late Yosef Ben-David, Michel Bitbol, Jed Buchwald, Catherine Chevalley, Robert Cohen, Olivier Darrigol, Alon Drory, Detleff Diirr, Gideon Freudenthal, Michael Friedman, James Fuchs, Ruthi Glasner, Galina Granek-Tiroshi, Gerald Holton, Don Howard, Roger Hurwitz, Tanya Karachentzeva, Amon Keren, Alexei Kojevnikov, Edward MacKinnon, Avishai Margalit, Edna Ullman-Margalit, Jiirgen Renn, Esther Rosenfeld, Cristoff Schmidt, Zur Shalev, Roger Stuewer, and Linda Wessels. I gratefully acknowledge the support of the National Science Foundation (grant numbers 9011053 and 9123124) and the support of the

Preface and Acknowledgments

xv

National Endowment for Humanities (grant number FA 31327-92) during my work on parts of this book. I am also grateful to David and Frances Dibner and the Dibner Foundation for the endowment of the Barbara Dross Dibner Chair in History and Philosophy of Science at the Hebrew University of Jerusalem, which I have the honor to hold. Part of chapter 7 is based on my joint paper with Arthur Fine (Beller and Fine 1994). Portions of chapters 2,4,6,8,9, 13, and 14 are based in part on my previously published articles (Beller 1983,1985,1990, 1992a, 1996a, 1997a, and 1997b). I am grateful to John Sanders for permission to quote materials from his collection (1987) of Bohr's published papers and unpublished manuscripts. The originals of Bohr's unpublished manuscripts are deposited in the Niels Bohr Archive in Copenhagen. They are available in microfilm in the Archive for the History of Quantum Physics (AHQP), copies of which are deposited in several universities throughout the world. I am grateful to Felicity Pors from the Niels Bohr Archive in Copenhagen for her assistance. I also want to express my gratitude to the librarians of the Van Leer Institute, Edelstein Library, and the Niels Bohr Library in the American Institute of Physics for their help. I also gratefully acknowledge the courtesy of the Emilio Segre Visual Archives in the American Institute of Physics for the photographs appearing in this book, and I thank Jack Scott, the photo administrator, for his helpful assistance. Very special thanks are due to my friend Shuli Barzilai, who returned two years ago from her trip to Russia with a unique souvenir-the photo she took of the statue of Einstein and Bohr in a park in Moscow. The photo decorates the jacket of this book. I am one of those lucky authors who has had the pleasure and the privilege of working with Susan Abrams, executive editor at the University of Chicago Press, and to benefit from her sharp mind and big heart. I am grateful to the wonderful staff at the University of Chicago Press: to Rodney Powell and Charles Clifton, editorial associates for the sciences; to Leslie Keros, who worked on the proofs; to Martin Hertzel, who designed the book; to Joan Davies, who supervised the production; and to David Aftandilian, who handled the promotion. I am also grateful to Diana Gillooly for her meticulous and dedicated work on the manuscript and to James Famed for the index. Last but not least, I want to thank my family for years of patience and support. My husband, Aaron, has always taken a caring interest in this work, providing uncompromising criticism and technical assistance. My gratitude to Aaron is beyond words.

CHAPTER 1 ~

Novelty and Dogma I believe that to solve any problem that has never been solved before, you have

to leave the door to the unknown ajar. You have to permit the possibility that you do not have it exactly right. Richard Feynman 1998, 26-27

A dialogue can be among any number of people, not just two. Even one person can have a sense of dialogue within himself, if the spirit of the dialogue is present. The picture or image that this derivation suggests is of a stream of meaning flowing among and through us and between us. David Bohm 1996, 6

Dialogical Creativity "Science is rooted in conversations." These words were written by Werner Heisenberg, a great physicist of the twentieth century and a founder of the quantum revolution (1971, vii). How exactly is science rooted in conversations? And how did an extended conversation among scientists result in the quantum revolution? These are the major issues of this book. Science is also rooted in doubt and uncertainty. "And it is of paramount importance, in order to make progress, that we recognize this ignorance and this doubt .... what we call scientific knowledge today is a body of statements of varying degrees of certainty. Some of them are most unsure; some of them are nearly sure; but none is absolutely certain. Scientists are used to this." These words belong to another great scientist of the twentieth century, the quantum physicist Richard Feynman (1998, 3, 27). "We know that it is consistent to be able to live and not know," continued Feynman: "I always live without knowing. That is easy. How you get to know is what I want to know" (1998, 27-28). How is the presence of uncertainty and doubt built into scientific theOrizing at its most basic level? How do scientists live without knowing? And how do they get to know? I argue throughout this book that the question of how scientists live in uncertainty, the question of how

2 Chapter One

they create their knowledge, and the question of how science is rooted in conversations are, in fact, one and the same. I elaborate an answer to this question for the case of the quantum revolution. This book examines the fluid, open-ended, and often ambiguous process of scientific creativity, treating it as being rooted in, and perhaps indistinguishable from, an ongoing scientific conversation about theories, experiments, and instruments. I address the central issue of how theoretical knowledge is achieved, articulated, and legitimated. I also deal with another major issue: the conceptual and emotional turmoil created by attempts to interpret the potent quantum formalism. I describe and analyze the intricate flux of dialogues among quantum physicists-dialogues that resulted in scientific breakthroughs of unprecedented scope and in a radical quantum philosophy. These dialogues underlay both the open-minded foundational research and the erection of the orthodox interpretation of quantum physics: the Copenhagen interpretation. Tracing the web of dialogues reveals a story about the workings of free scientific imagination and about the consolidation of scientific dogma. One of the major puzzles in the history of quantum physics is the existence of numerous contradictions in the Copenhagen interpretation. What is the source of these contradictions? And why are they impotent to detract from the spectacular power of quantum physics? A large part of this book constitutes an answer to these questions. The analysis and the narrative in this work are permeated with the notion of communicability. I argue that dialogue underlies scientific creativity and that the emergence of scientific novelty cannot be understood without scrutinizing the ways scientists respond to and address each other. This book analyzes the complex, multidirectional dialogical nature of scientific theOrizing (part 1) and the strategies by which this dialogical flux is flattened into a monological narrative (part 2). This book is based on a close study of primary sources-correspondence between the participants, notebooks, original papers. Historians of quantum physics are fortunate to have access to the Archive for the History of Quantum Physics (AHQP), where correspondence and original manuscripts are collected. Thus I had the opportunity to study in detail the intricate paths along which ideas emerged as the founders of quantum physics addressed each other in their letters. I gradually realized that dialogical addressivity permeates not only scientific correspondence but also published scientific papers, and more generally, I came to the realization that scientific creativity is fundamentally dialogical in the sense elaborated in this book. The dialogical approach to the history of science is "bottom up" -it searches for the most basic details in order to conceptualize the process

Novelty and Dogma

3

through which knowledge grows. A dialogical analysis, by closely following ideas as they gradually form in numerous dialogues between scientists, deals primarily with the cognitive content of science. It requires painstaking attention to every nuance of the primary sources. In fact, it demands closer attention to the minutia of scientific reasoning than the older, "internal" (evolutionary) history of science and than "rational reconstruction" accounts. My exposition differs from the usual accounts by describing the flux of ideas without presupposing underlying conceptual frameworks, schemes, or paradigms. In fact, these notions, whether on a global or a more restricted scale, are not easily compatible with the dynamics of ceaseless scientific change. Living in doubt and uncertainty is not compatible with the accepted histOriographical notions of "beliefs" and "commitments." Nor are Kuhnian and post-Kuhnian "agreement" and "consensus" suitable to describe the dynamics of living without knowing. Doubt and uncertainty should be incorporated into the basic terms used to describe the growth of knowledge. From the dialogical perspective, it is "creative disagreement"-with oneself (doubt) or with others (lack of consensus )-that plays the crucial role in the advance of knowledge. The privilege to be unsure, to theorize freely, to explore different options at the same time, is incorporated into the notion of creative dialogical flux. I will elaborate on the philosophical, historiographical, and sociological advantages of such a dialogical approach in the concluding chapter of the book. This book simultaneously revises the story of the quantum revolution and outlines a tentative program for a dialogical historiography of science. My work began with a revision of the history of matrix mechanics (Beller 1983) and progressed to revisions of other major episodes in the history of quantum physics, such as the emergence of Born's probabilistic interpretation (Beller 1990) and the birth of Bohr's complementarity (Beller 1992a). It gradually became clear to me that the need for ongoing revision has a fundamental historiographical cause. This cause is intimately connected with the complex dialogical nature of thought and with the strategies used to flatten it into linear monological narratives. I begin my description of the quantum revolution with an analysis of matrix theory in flux (chapter 2), arguing against the received story of the existence of two totally distinct theoretical frameworks-the matrix and the wave theoretical. In chapters 2 and 3 I describe how a strong distinction between the matrix and wave approaches crystallized as the end result of a conceptually fascinating and emotionally intense confrontation among quantum physicists. In the fruitful ambiguity of the newly created knowledge, there was no place for strong "beliefs" in

4

Chapter One

indetemtinism or "commibnents" to positivism. Nor is it correct to see the matrix theoreticians as committed to a particle ontology, as opposed to Schrodinger's wave approach. We will see that Heisenberg's, Born's, and Pauli's pronouncements on foundational and interpretive issues were all fluid and uncommitted. Similarly, I will argue, Born's probabilistic interpretation did not stem from his "belief" in particles and "commitment" to indeterminism, as the received history of quantum physics implies (chapter 2). The flux of ideas in the emergence of matrix theory and in the formation of Born's probabilistic interpretation demonstrates the primacy of mathematical tools over fundamental interpretive ideas. These tools can be borrowed, developed, and successfully applied without a clearcut stand on basic interpretive issues. It was on the efficiency of the mathematical tools, and not on metaphysical "paradigmatic" issues, that there was agreement in the community of quantum physicists. And on this point the orthodox and the opposition were united; agreement on the potency of these tools prevented scientific practice from disintegrating, be the philosophical disagreements as large as they may. Theoretical tools (equations, methods of solution, and approximations) have their own momentum, while philosophical ideas are adapted a posteriori (chapter 3). The fact that theoretical tools have some autonomy allows scientists to theorize without taking an interpretive stand. The English physicist Charles Darwin wrote to Niels Bohr: "It is a part of my doctrine that the details of a physicist's philosophy do not matter much" (Darwin to Bohr, December 1926, AliQP). This belief in the primacy of mathematical tools was especially strong in COttingen, inspiring Born's and Heisenberg's search for a new quantum theory. "Mathematics knows better than our intuition" was Born's motto (interview with Born, AHQP). The neutrality of a mathematical formalism with respect to possible interpretations has another far-reaching consequence: scientists may give all authority in interpretive matters to a few leaders, whose philosophy they are willing to accept. Such humble resignation from philosophical exploration is often nothing but a convenient choice not to deal with confusing and perhaps irrelevant matters.1 It is this attitude that creates room for an authoritative and privileged interpretation, such as the Copenhagen orthodoxy. 1. This position was taken by Darwin: '1'm quite ready in advance to believe that your criticisms are quite right, but I feel that perhaps this does not matter mudt. Because the best sort of contribution that people like me can make to the ~ject is working out of problems, leaving the questions of principles to you. In fact even if the idea:; on which the work was done are wrong from the beginning to end, it is hardl}' possible that the work itself is wrong in that it can easily be taken over by any revised fundame(ltal ideas that you may make" (Darwin to Bohr, December 1926, AHQP).

Novelty and Dogma

5

The dispensability of paradigmatic interpretive agreement also explains what Steven Weinberg, not without a touch of disdain, called "the unreasonable ineffectiveness of philosophy" in scientific practice (Weinberg 1992, 169). The application of theoretical tools involves flexibility and conceptual opportunism-no system of philosophical preconceptions can survive in such a fluid environment (chapter 3). Philosophical"influence" indeed cannot determine a scientific knowledge claim. Yet philosophy can be suggestive in a limited way, as inspiration along some path in the dialogical web of creativity. In chapter 4 I argue that the ideas of the German philosopher Fichte were important for Heisenberg's treatment of measurement in the uncertainty paper. This treatment, or "reduction of wave packets," became the source of the major conceptual hurdle of quantum physics-the notorious measurement problem. Scientific creativity as a dialogical flux is exemplified by the emergence of Heisenberg's uncertainty principle, which I describe in chapter 4. We can see how Heisenberg theorized without a clearly delineated conceptual framework, without "beliefs" and "commitments." Instead, we observe the indispensability of open-ended disagreement and ongoing doubt for achieving a theoretical breakthrough. The existing historiography presents one-dimensional pictures: Jammer described the uncertainty formula as emerging naturally from the imperative to adapt the new mathematical formalism to the possibilities of measurement (Jammer 1966).2 The perspective offered by social historians similarly focuses only on a single aspect: a predilection for acausality among quantum physicists determined their efforts to interpret the new quantum mechanics along probabilistic lines (Forman 1971; Feuer 1963). I describe Heisenberg's discovery of the uncertainty relations as a multidirectional process, which took place in a communicative network with many interlocutors, including such prominent names as Einstein, Schrodinger, Pauli, Dirac, Bohr, Born, and Jordan. Less known, yet no less important for Heisenberg's discovery, are the names Campbell, Duane, Zernike, and Sentfleben. In chapter 4 we follow the process of discovery and observe how fragments of insight gradually emerge, how ideas clash, change, disappear, or survive. The gradual forming of a preference, of choosing one intellectual option over another, of defining what the options are-all occur in a coalescence of insights, arrived at in different dialogues and at different times. Heisenberg's discovery of the uncertainty principle was a complex 2. Jammer described the controversy between Bohr and Heisenberg with respect to the uncertainty paper as a tool for elucidating Bohr's and Heisenberg's respective positions and as anecdotal history. From Jammer's analysis it is not clear how the disagreements contributed to the creation of uncertainty and complementarity.

6

Chapter One

process of disagreements, qualifications, elaborations, supplementations, and borrowings. He had no foundational commitments, even on such basic issues as discontinuity and indeterminism; rather his preference for discontinuity and acausality took shape gradually in many fruitful dialogues. Though immersed in interpretive efforts, Heisenberg was uncertain even about what the word "interpretation" means (chapter 5). Disagreements with interlocutors-a militant one with Schr5dinger, a subdued yet painful one with Bohr, a restrained one with Jordan and Born-were triggers for Heisenberg's reasoning. Agreement too played a part, in the form of Heisenberg's partial, often only temporary, acceptance of the ideas of others, especially those of Dirac, Campbell, and Duane. Heisenberg's case demonstrates how genuine novelty emerges through dialogical creativity. Dialogical creativity is not an instantaneous "eureka" experience; it is rather a patiently sustained process of responsiveness and addressivity to the ideas of others, both actual and imagined. One might expect that in a published scientific paper, all previous cognitive tensions would be resolved and a coherent unequivocal message expressed. Yet an analysis of Heisenberg's uncertainty paper finds clear traces of past struggles, conflicting voices on the same issue, and unresolved tensions (chapter 5). The polyphony of the creative act echoes in the paper itself. Similarly, at least two conflicting, in fact incompatible, voices can be heard in Bohr's response to Einstein-PodolskyRosen's challenge to the Copenhagen interpretation (chapter 7). One might object, then, that such unresolved tensions perhaps characterize scientific papers written during revolutionary upheavals, but when things settle down and the revolution is over, a new paradigm triumphs and the foundational debate is closed. There is, the argument might continue, at the present time only one correct, agreed-upon meaning of the uncertainty principle and of wave-particle complementarity. But is there? One can find a "correct" meaning in textbooks, or in some philosophical writings on the quantum theory-in short, in the graveyards of science. On the research frontier nothing is immune to reappraisal-be it uncertainty, complementarity, or even the determinism of classical physics (chaos theories) and the indeterminism of quantum physics (Bohrn's theory and Bohrnian alternatives, such as Diirr, Goldstein, and Zanghi 1992a, 1992b, 1996). Numerous meanings of the uncertainty formulas are proposed in current research papers (Home and Whitaker 1992; Valentini 1996). The same is true of Born's probabilistic interpretation and his solution of the collision problem (Daumer 1996). Similarly, there is no agreement about the meaning or even the validity of wave-particle complementarity (chapter 11). Even such basic formulas as Schrodinger's equation are open to modification (Ghirardi,

Novelty and Dogma

7

Rimini, and Weber 1986). The flux of creative research cannot be forced into an unequivocal, final conceptual scheme. The description of Heisenberg's creative theorizing calls for a reevaluation of the role of "lesser" scientists in the growth of scientific knowledge (chapter 4). We will see that some of the most important insights pertaining to Heisenberg's formulation of the uncertainty principle belonged to scientists whose names do not appear in the received history of quantum mechanics-Sentfleben and Campbell. The issue is not one of priority, even though the distribution of credit is often unfair. Neither Campbell nor Sentfleben, from their positions in the communicative web, could have accomplished exactly what Heisenberg did. Yet neither could Heisenberg have developed his ideas had he not been responding creatively to Campbell's and Sentfleben's insights. Heisenberg's discovery is organically linked to the ideas of the "lesser" scientists. From the epistemological point of view, the notion of a scientific collective is intrinsic to the dialogical approach. We can reevaluate the prevalent idea of a lonely creative individual, and of solitude as a precondition of creativity. Conventional opinion holds that "the spark of creativity burns most brightly in a mind working in solitude" (Storr 1988). When Heisenberg "fabricated" the new quantum mechanics (his expression, van der Waerden 1967, 15), he was isolated on the island of Helgoland. After their stormy debates on the interpretation of quantum mechanics in the fatefu I year of 1926, Heisenberg and Bohr needed to get away from each other. Separated, Heisenberg wrote the essentials of his uncertainty paper and Bohr elaborated his complementarity. Yet solitude does not imply cognitive isolation. If Heisenberg needed time away from Bohr, it was in order to strike a proper, uncoerced balance in his own communicative network of cognitive responses (chapters 4 and 6). The dialogical perspective provides a new way to read published scientific texts. Concealed doubt becomes visible, and a paper becomes a fascinating scientific and human document, resounding with conflicting inner voices, populated by many "virtual" interlocutors (chapters 5 and 6). We will see in chapter 5 that Heisenberg's uncertainty paper is permeated with doubts and indecision on such central issues as indeterminism, realism, visualizability, and the status of classical concepts in the quantum domain. A comparison of the (seemingly) confident published paper with the almost identical draft (in a letter to Pauli) filled with doubt regarding all the basic interpretive issues reveals how misleading it is to ascribe any "beliefs" or "commitments" to Heisenberg. My analysis applies to the issues of acausality and positivism that according to the accepted history of quantum physics, are the two central pillars of Heisenberg's uncertainty paper.

8

Chapter One

My examination of Heisenberg's uncertainty paper reveals the argumentative strategies by which interpretive freedom is concealed, and the illusion created that the orthodox interpretation is "inevitable"the issue to which the bulk of part 2 of this book is devoted. Tension between the conceptual freedom experienced by the Copenhagen physicists and their desire to advocate one privileged interpretation is one of the major sources, I argue, of the numerous contradictions and inconsistencies in the Copenhagen interpretation of quantum physics. Yet the dialogical analysis of a published paper does more than reveal the inconclusive nature of scientific theorizing. Such an analysis can also substantially modify our understanding of the content of a published paper. A dialogical reading is a potent tool for deciphering especially obscure and opaque texts. Chapter 6 is devoted to a dialogical analysis of Bohr's Como lecture, in which Bohr announced his principle of complementarity. The Como lecture is considered one of the most incomprehensible texts in twentieth-century physics. My dialogical reading constitutes a basic revision of the accepted reading of this text, by presenting the Como lecture, not as the unfolding of a single argumentative structure, but as the juxtaposition of several simultaneously coexisting arguments, addressed to different quantum theorists about different issues. A dialogical analysis reveals that the central message of Bohr's paper was not the resolution of wave-particle duality by the complementarity principle, as usually assumed, but rather Bohr's extensive defense of his concepts of stationary states and discontinuous energy changes (quantum jumps) against Schrodinger's competitive endeavors. A dialogical reading allows the reevaluation of some central events in the history of quantum physics, such as the famous clash between Heisenberg and Bohr over the uncertainty paper. This reevaluation merges "motives" and "reasons," connecting "conceptual" and "anecdotal" history into one meaningful, comprehensible story. This story throws new light on Einstein's and Schrodinger's initial reservations about the early interpretive attempts of Bohr and Heisenberg-reservations due to difficulties and contradictions in the emerging Copenhagen interpretation rather than to Einstein's and Schrodinger's "conservatism." My analysis of the initial efforts of Bohr and Heisenberg to unveil the physical meaning of the quantum formalism demonstrates the vast freedom of interpretive endeavors. Yet this freedom is not arbitrary. We will see the great extent to which the formulations of Born's probabilistic interpretation, Heisenberg's uncertainty, and Bohr's complementarity were woven around detailed analyses of experimental situations (a fact not sufficiently apparent in the existing histories of quantum

Novelty and Dogma

9

mechanics). These first attempts at interpretation revolved around pivotal experiments by Franck and Hertz (1913), Bothe and Geiger (1925a, 1925b), and Compton (1923), as well as around experimental work by the lesser known Moll and Burger (1925). There is a crucial difference between evidence-based interpretive efforts and closed dogmatic systems, although the first can degenerate into the second, as with Bohr's, Heisenberg's, and Pauli's later philosophical writings, which came close to preaching a rigid ideology (part 2). Chapter 7 (the last chapter of part 1) analyzes the process by which sincere and open-minded, though interest-laden, interpretive attempts hardened into an ideological stand intended to protect quantum theory from challenge and criticism. This chapter, partly based on my paper with Arthur Fine (Beller and Fine 1994), is devoted to an analysis of Bohr's reply to the Einstein-Podolsky-Rosen (EPR) challenge. This chapter is located, so to speak, on a "cut" between parts 1 and 2 and can be moved from the end of part 1 to the beginning of part 2 without distorting the argument of my book. This means that dialogical emergence and rhetorical consolidation are not completely distinct processes. Consolidation was already present in the initial interpretive attempts of the Gottingen-Copenhagen camp, and limited dialogical responsiveness accompanied later elaborations of the Copenhagen interpretation. Still, chapter 7 reveals a vast difference between Bohr's reasoning in his Como lecture and his reply to the EPR challenge. My analysis uncovers a transition from legitimate, though often confused, arguments for the consistency of quantum theory, to argumentative strategies promoting the inevitability of the orthodox stand. This transition naturally contains both old insights and new conquests, and it is not surprising that two different, often incompatible voices permeate Bohr's response to EPR. The voices correspond to Bohr's two different answers to EPR: one relying on the concept of disturbance, the other dispensing with it. In contrast to the received story, which, following the orthodox narrative, affirms Bohr's "victory" in this confrontation, the analysis in chapter 7 reveals that none of Bohr's answers can be considered satisfactory. I further analyze Bohr's about-face on the central interpretive issuesthe problems of reality, acausality, and measurement-raised by the EPR challenge. I extend this analysis in chapter 8, arguing that the Copenhagen interpretation is in fact a compilation of various philosophical strands, given a public presentation that often hid shifting disagreements between its main architects. The Copenhagen interpretation of quantum physics did not originate from a disinterested search for philosophical foundations-from the very beginning it was constructed in the heat of a fierce confrontation. As the nature of the opposition's challenge changed, so did the local responses of the orthodox. It is not

10

Chapter One

surprising therefore that what is called the Copenhagen interpretation is so riddled with vacillations, about-faces, and inconsistencies (chapter 8). The orthodox aimed to present a united front to the opposition, concealing the substantial differences of approach among its members. I analyze some of the strategies by which such differences were suppressed by relying on a distinction between what scientists "must not" and what scientists "need not" do (chapter 8). Rhetorical Strategies How does one construct from among these numerous contradictory arguments a narrative that seems to irrevocably imply the pillars of the Copenhagen dogma? How does one reconstruct history so that the central tenets of the Copenhagen interpretation, such as indeterminism and the impossibility of an objective, observer-independent description, seem not merely highly persuasive but outright inevitable? In part 2 of the book I contend that all the Copenhagen arguments of "inevitability" are in fact fallacious-they rely either on circular reasoning or on highly appealing but misleading metaphorical imagery (chapters 9 and 12). They are strongly supported by falsified history, which renders certain developments as dictated by the inner logic of the development of ideas (chapters 10 and II). Discrediting the opposition and caricaturing the opposition's criticism of the Copenhagen stand is yet another potent rhetorical device to strengthen the orthodoxy (chapter 13). These chapters reveal how fruitfully ambiguous and wisely uncommitted interpretive efforts are concealed by rigid reconstructed stories. Complex, many-voiced, multidirectional theOrizing is thus conflated into an orthodox, one-dimensional narrative. ''History is written by winners"-this cliche finds powerful confirmation in the case of the quantum revolution. We have numerous reminiscences by the winners-Bohr, Heisenberg, Born, Jordan, and others. There are hardly any reminiscences by Einstein and Schrodinger about the same events-we do not hear the opposition's side of the story. In the quantum revolution, the orthodox constructed the narrative, eliminating dissident voices and largely suppressing the crucial contributions of the opposition and of lesser scientists. In part 2 I describe the strategies by which the past is manipulated in order to make the winners look naturally right. By such a reconstruction of the past, the cornerstones of the Copenhagen interpretation-quantum jumps, the impossibility of causal space-time models, indeterminism, and waveparticle complementarity-were even more firmly entrenched (chapters 10 and 11). I describe how the opposition's stand is delegitimated and trivialized. In their fabricated narratives, the winners construct the profile of the

Novelty and Dogma

11

opposition and the description of past science concurrently. The ideas of the opposition are projected as most characteristic of the overthrown past, and thus the opposition naturally appears reactionary-disposing of the old and discrediting the opposition are, in fact, one and the same process. As a result, not only is the opposition caricatured but past science is trivialized. Hero worship of the winners further delegitimates the opposition and prevents criticism of the orthodox stand (chapter 13). Historians of science rarely question the narrative of the winners: Jammer (1966) and Mehra and Rechenberg (1982), for example, closely follow the orthodox line. Jammer, in the preface to his classic book, quotes Einstein's penetrating warning not to rely on the recollections of the participants: "To the discoverer in this field the products of his imagination appear so necessary and natural that he regards them ... not as creations of thought but as given realities." Yet Jammer "felt entitled to ignore this warning," and he "discussed the subject with quite a number of prominent physicists who contributed decisively to the development of the theory" (1966, viii). Pais's recent book (1991) is written exclusively from Bohr's perspective. This is not to say that these accounts do not use primary sources; in fact, Jammer, Mehra and Rechenberg, and Pais use the sources extensively. Yet what they see in those sources, and more important, what they ignore therein, is dictated by the overwhelming authority of the winner's perspective. A notable exception in this respect is Cushing's (1994b) important book about Bohmian mechanics as a viable alternative to the Copenhagen hegemony. The "naturalness" and even "finality" of the orthodox point of view is advanced through powerful strategies of persuasion, which I refer to as the "rhetoric of inevitability" (chapter 9). The ingenious technique was to disguise arguments of consistency as those of inevitability. What is taken as objective quantum philosophy (and "inevitable" at that) turns out to be ideology-where by ideology I mean a system of assertions that imply, from within, their own justice, truth, and selfevidence. With respect to the entrenchment of the Copenhagen dogma, epistemology and sociology often merge-considerations of epistemic warrant and of social legitimacy are, at times, indistinguishable. The foundations of the Copenhagen paradigm were chosen and elaborated in direct contrast to the opposition's stand. The construction of the winner's narrative and philosophical arguments of inevitability serve the same end. In chapter 11, I contrast the dramatic narrative of the "inevitability" of wave-particle complementarity with the freedom and plurality of theoretical approaches to the wave-particle issue. The "logical" arguments for the inevitability of wave-particle complementarity are built on Bohr's peculiar doctrine of the "indispensability" of classical

12

Chapter One

concepts-a doctrine that few theorists, including Bohr's closest collaborators, found persuasive (chapter 8). Those mathematical physicists who gave up this rigid doctrine suggested a rich variety of solutions to the wave-particle dilemma (chapter 11). The discussion in chapter 11 demonstrates that there is a fundamental ambiguity, and therefore a lack of" paradigmatic" agreement, concerning even such basic physical terms as "wave" and "particle" (scientists hold different opinions, each from his own theoretical viewpoint, of what are to be considered necessary or sufficient attributes of those terms). Despite this lack of clarity, or perhaps because of it, conversation on this issue continued, and new theoretical breakthroughs occurred. The same freedom that created room for open-ended creative theorizing allowed the construction of a variety of ad hoc strategies for the legitimation of the Copenhagen stand. The proliferation of such ad hoc moves is yet another source of the inconsistencies that still plague the Copenhagen interpretation today. Both Heisenberg and Pauli supported Bohr's philosophy of wave-particle complementarity in public, while often expressing, behind closed doors, views that were contrary to Bohr's. Heisenberg, Born, and Pauli, as well as Bohr himself, exploited wave-particle complementarity for pedagogical and ideological reasons. The simple thought experiments that supposedly demonstrated the necessity of both the wave and particle descriptions were especially effective for promoting the philosophical "lessons" of quantum theory to wider audiences. From the analysis of these experiments, supported by Bohr's doctrine of the indispensability of classical concepts, both the "finality" of indeterminism and the "impossibility" of unified objective description followed, leaving seemingly no possibility of other interpretive options. The accessibility of the explanatory strategies fed the illusion that no technical understanding of the quantum mechanical formalism is needed in order to grasp the essence of the quantum revolution. 3 This illusion was most vigorously sustained by Bohr himself. "Philosophy is but a sophisticated poetry"-this view of philosophy aptly characterizes Bohr's voluminous improvisations on the theme of complementarity, filled with affective analogies, subjective associations, and allusions to "harmonies," expressed in "common language." In chapter 12, I argue that Bohr's philosophy is best characterized as a richly imaginative, yet ultimately misleading attempt to comprehend the quantum mystery without recourse to the mathematical formalism of quantum theory. There is, in this sense, a vast difference between the complementarity principle and Bohr's correspondence principle, which 3. Many postmodemist critics of science fell prey to the temptations of this strategy of argumentation (Beller 1998).

Novelty and Dogma

13

guided the search for the new quantum theory in the early 1920s, and with which the complementarity principle is sometimes confused. The metaphors of the complementarity principle are vague and arbitrary, in contrast to the more rigorous use of analogies between the macro- and microdomains guided by the correspondence principle. While the correspondence principle was a potent heuristic that led to the discovery of the rigorous quantum formalism, the complementarity principle was a device of legitimation-it led to no new physical knowledge. In chapter 12, I analyze the ways Bohr, Pauli, and Heisenberg, by their imprecise allusions to quantum "wholeness," spun a metaphOrical web of associations that disguise, rather than reveal, quantum entanglement and nonlocality. I argue that these allusions and analogies are fed by classical intuitions and contain nothing quantum about them. Not surprisingly, Bohm's version of quantum theory and its recent variants, which fundamentally incorporate quantum wholeness as a basic principle, are compatible with deterministic description. Bohr's numerous opaque allusions to quantum wholeness contribute to the illusion that his philosophical views were stable, despite the fact that he used this notion differently in different contexts. The notion of wholeness undergoes especially drastic change between Bohr's pre-1935 and his post-1935 writings (as a result of EPR). This ingenious and misleading improvisation on the idea of quantum holism contributes to the deception that a well-defined philosophical framework exists, thus further entrenching the Copenhagen orthodoxy. Support for the orthodox view comes not only from historians but from philosophers of science as well. The strongest support came from Norwood HanSon and, after him, Thomas Kuhn. who incorporated the Copenhagen ideology into an overarching theory of the growth of scientific knowledge (chapter 14). Hanson and Kuhn canonized the concepts of paradigm and incommensurability into objectified philosophical notions that exclude, in principle, diversity of opinion and legitimate disagreement. Thus opposition is discredited and eliminated in the most radical way-by definition. Kuhn and sociologists of science who follow Kuhn's approach talk in terms of "deviance" and "impermissible aberration" rather than acknowledging reasonable disagreement. Kuhn's theory of incommensurable paradigms and the orthodox narrative of the quantum revolution reinforce each other-the quantum revolution is cited as a prime example supporting Kuhnian philosophy,4 and the orthodox narrative of the quantum revolution is 4. Even historians who question the adequacy of Kuhnian notions to describe other historical developments (Westman 1994, discussing the Copernican-Newtonian revolution) assume that Kuhn's philosophy adequately describes the case of the quantum revolution.

14

Chapter One

objectified by a Kuhnian theory of the growth of knowledge (chapter 14). By such circular argumentation. the orthodox perspective is made to appear unassailable. By incorporating addressivity and disagreement as fundamental notions, the dialogical approach, developed here, presents an alternative to current approaches to the study of science. Dialogical analysis incorporates conversation and communicability both as social realities and as epistemological presuppositions. From the dialogical perspective, a creative scientist cannot, in principle, be isolated-he, or she, is linked fundamentally to the efforts and concerns of others. In the dialogical approach, the notorious question of whether science is "rational" or "social" in nature becomes a pseudoproblem. Science is simultaneously rational and social-the rationality of science is dialogical and communicative. The view of scientific activity as an ever-changing, open-ended communicative flux fits well scientists' own image of their work. Theoretical physicist David Finkelstein (1987), describing the state of his discipline today, chose the Heraditean "All is flux" for the title of his paper. David Bohm emphasized the essential communicability of scientific doing: "Communication plays an essential role in the very act of scientific perception.... They [scientists] constantly engage in a form of internal dialogue with the whole structure of their particular discipline.... When insight occurs, it emerges out of this overall structure of communication and must then be unfolded so that it obtains its full meaning within it" (Bohm and Peat 1987,67). In the conduding chapter of this book I provide a tentative outline for a dialogical historiography and philosophy of science. Dialogical historiography reestablishes scientific individuality as the focus for studies of the growth of knowledge. Dialogical analysis demonstrates that scientific theorizing can be both free and nonarbitrary, and that theoretical achievements can be simultaneously well grounded and imaginatively beautiful. We constantly conduct conversations with others-with living people, with the dead, and even with the yet unborn. The Russian poet Marina Tsvetaeva, in one of her poems, addressed a reader one hundred years in the future-the one who wilI truly love and understand her, and who will prefer her remains to the flesh of the living. Without unceasing addressivity and communicability, existence and thought, artistic imagination and scientific creativity are inconceivable.

PART ONE 1::;::::1

Dialogical Emergence

CHAPTER 2 ~

Matrix Theory in Flux Antagonistic cooperation is the key. William Carlos Williams 1936, 177

Introduction

The years 1925-27 were a time of astounding scientific creativity. Dirac (1977) referred to this time as the "exciting era/' while Pauli called it a "period of spiritual and human confusion" (1955a, 30). It was both. The "exciting era" refers to the breathtaking advances in the foundations of physics, "human confusion" to the treacherous matter of interpretation, to intensely emotional confrontations, to the slippery philosophical implications of the new conceptual tools. In this period of unprecedented advance the openness and ambiguity of theoretical practice seemed "confusing." But perhaps it was this ambiguity that created conceptual room for such rapid progress. There was no strong "belief" either in indeterminism or positivism, as the received story implies-pronouncements on these issues were uncommitted, fluid, and opportunistic. The human confusion is reflected in the rich folklore of the history of quantum physics-anecdotes about inflamed passions and wounded egos, about emotional strain and outspoken hostility. These emotions produced not merely heat-they begot light (Beller 1996b). In this chapter I analyze the initial efforts to interpret the new matrix formalism. I also describe the emotional confrontation between the matrix physicists and Schrodinger, which fused, or confused, issues of foundational preference with that of professional privilege. I argue that the emergence of Born's statistical interpretation of quantum mechanics was devoid of prior philosophical preferences and was embedded in the dialogical context of the ''battle'' between Schrodinger and the Gottingen-Copenhagen camp. This chapter and the following one undermine the myth that the matrix and wave approaches were from the beginning conceptually distinct and historically independent. I argue that the strong distinction, and even polarization, of the wave theoretical and matrix approaches developed as a result of the confrontation between the

18

Chapter Two

competing groupS.l This being the case, physicists on both sides were not generous in their papers and later recollections with acknowledgments of mutual debts. A Revision of the Origins of the Matrix Theory The still widely accepted scenario for the development of the new quantum mechanics in the 1920s runs as follows. In a period of only a few months (late 1925 to early 1926), two major theories of atomic phenomena emerged: matrix mechanics and wave mechanics. Matrix mechanics originated in Werner Heisenberg's radical reinterpretation of basic physical magnitudes (Heisenberg 1925), and Max Born, Pascual Jordan, and Heisenberg immediately expanded it into a complete and logically consistent theoretical structure in the so-called Dreimannerarbeit (Born and Jordan 1925a; Bom, Heisenberg, and Jordan 1926). Wolfgang Pauli (1926b) demonstrated that the abstract formalism of matrix mechanics gave the correct approach to atomic theory by solving the problem of the structure of the hydrogen atom-the central problem of the atomic domain. The basic concept of matrix theory was the particle, or corpuscle. 2 The basic concept of the rival theory, Erwin Schrodinger's (1926a, 1926b, 1926c, 1926d,1926e, 1926f), was instead the wave, based on ideas first proposed by Louis de Broglie (1923). Schrodinger's theory combined intuitive and adequately developed mathematical tools with familiar physical concepts, and it was enthusiastically welcomed by the conservative wing of the physical community, which distrusted the revolutionary physical ideas of matrix mechanics and the complicated mathematics involved. Though radically different in their basic assumptions and mathematical treatments, the two theories were soon proved to be equivalent by Schrodinger himself,3 and the only major problem left was that of physical interpretation. Schrodinger attempted to ascribe to his theory a classical, continuous wave interpretation, but the quantum physicists at Gottingen and Copenhagen demonstrated that these conservative attempts were untenable. The physical interpretation that prevailed instead was a direct continuation of the indeterministic beliefs of Heisenberg, Born, and Niels Bohr. 1. This book analyzes the Gottingen-Copenhagen side of the confrontation. An analogous argument can be made about Schrodinger. It is explored in part in Wessels (1983). I am currently exploring Schrodinger's case as weU. 2. See also Darrigol (1992a), Jammer (1966), and Mehra and Rechenberg (1982). 3. Recently, MuUer (1997) chal1enged the "myth of equivalence." He claimed that there was no strict equivalence between Schrooinger's and Heisenberg's versions originallythe two theories became truly equivalent after von Neumann's formalization of transformation theory.

Matrix Theory in Flux

19

Contrary to this story, I have argued that matrix mechanics was not immediately recognized as a pivotal breakthrough (Beller 1983). A few months before the publication of Schrodinger's mechanics and its use in transformation theory, matrix mechanics was beset by difficulties of such magnitude that no one, including the authors themselves, considered it to be more than a first step on a long path toward the ultimately correct theory. This was the main reason for the enthusiastic acceptance of Schrodinger's theory: acclaim for Schrodinger's theory was not limited to the conservative quarters of the physical community. Nor was matrix mechanics a theory of corpuscles before Born's probabilistic interpretation: an atom in the matrix approach was endowed with electromagnetic, not kinematic, meaning. It is impossible to understand the genesis of the philosophy of quantum mechanics without closely following the original interpretive announcements of matrix phYSicists and the modifications they later underwent in dialogical response to Schrodinger's theory. The radical assumption of the matrix approach-within the atom there is no geometry-evolved into the more moderate: within an atom there is only statistics. The classical space-time container, eliminated by the matrix approach, was restored in response to Schrodinger-first by Born, then by Pauli and Jordan, and finally by Heisenberg himself. It is easy to overlook this process because of the speed with which it took place. The resulting quantum philosophy evolved into a hybrid of the original radical matrix program, concepts revived from Bohr's earlier work, and statistical compromises necessitated by the acceptance of Schrodinger's continuous theory. The philosophy of quantum physics became a mixture of quantum and classical concepts, whose inherent difficulties plague physicists and philosophers to the present day.

Problems of Physical Interpretation: The Elimination of Space-Time Matrix mechanics, designed to avoid the problems of the old quantum theory, implied a radical change in the conventional description of the space-time continuum used in earlier physical theories. Heisenberg's 1925 paper-the turning point in quantum physics-announced the aim of eliminating unobservables and dispensing with visualizable models that relied on continuous space-time pictures. Instead of such unobservable kinematic variables as an electron's position, velocity, and period of revolution, Heisenberg sought to incorporate only observable spectroscopic data into the theoretical framework. 4 Heisenberg and his colleagues at Gottingen justified their approach 4. Although Heisenberg did not rely on it explicitly, the "virtual oscillator" model. which contradicted the usual picture of space-time within the atom, played an important heuristic role (MacKinnon 1977).

20

Chapter Two

by arguing that the difficulties of the old quantum theory stemmed from the fact that the quantum calculation rules operated with unobservable quantities-they were based on impennissible classical mechanical pictures, the use of which made the old theory inadequate for solving any but the simplest cases and led to grave inner contradictions (Heisenberg 1925). The Gottingen program was then to replace the explanatory mode of continuous classical mechanics with a discrete descriptive approach. Born had made a pivotal contribution toward a "truly discontinuous" theory by inventing a method (used in Heisenberg's reinterpretation paper) of replacing all differential coefficients with the corresponding difference quotients (Born 1924; Born, Heisenberg, and Jordan 1926). This replacement reflected the growing realization that in the new quantum theory each physical quantity should depend on two discrete stationary states, and not on one continuous orbit as in classical mechanics.s The old quantum theory chose certain stationary states from all possible mechanical motions by means of quantization rules. The new theory, Born emphasized, was to contain only the permissible values: consistency demanded that forbidden fractional values should have no meaning at all in the theory. This approach implied the elimination of classical space-time as a container of motion-such a container is as superfluous as the unrealized mechanical motions: "No one has been able to give a method for the determination of the period of an electron in its orbit or even the position of the electron at a given instant. There seems to be no hope that this will ever become possible, for in order to determine lengths or times, measuring rods and clocks are required. The latter, however, consist themselves of atoms and therefore break down in the realm of atomic dimensions" (Born 1926a, 69). Heisenberg admitted later that he intended to eliminate not only the orbits of bound electrons but even the experimentally observable paths of free electrons, despite Wilson's experimental substantiation of the latter (Heisenberg 1933,292). The authors of matrix mechanics initially implied not only that it is meaningless to represent electron motion as 5. According to Born, one cannot visualize atomic phenomena as continuous processes in space (for example, as orbital motion) because space itself is not infinitely divisible: there exist ultimate units of matter that cannot be further divided. Born derived this stand that nature has a scale and that one should not expect to find smaller and smaller elements not so much from the presupposition that matter is corpuscular as from the special form of quantum laws, in which only whole numbers appear. If physical laws are expressions of relations between whole numbers, more accurate measurement does not add any new information, and therefore physicists have reached the bottom of nature's scale (Born 1926a,2).

Matrix Theory in Flux

21

a change of position in time but also that it is impossible to ascribe position to an electron at a given instant. Space-time exists only in the macroscopic domain-in the atomic domain "space points in the ordinary sense do not exist" (Born 1926a, 128). This approach was tantamount to giving up all hope of devising a visualizable physical interpretation for the new matrix mechanics. As Jordan put it later, there is no reason to expect that mathematical relations between observable radiation entities are amenable to visualization built on classical habits (1927a, 648). Matrix mechanics is no more open to visualization than Maxwell's equations-one can only get used to manipulating both. The only physical interpretation to be expected from such an approach is the description of the limiting case of transition from the essentially unvisualizable quantum domain to the visualizable macroscopic world. 6 Even though Heisenberg and his colleagues could dispense with the demand for visualization on the atomic level, they still needed to comprehend the transition from microdomain to classical macrodomain. Yet the problem proved unyielding, and Heisenberg complained to Pauli about his failure to understand how to achieve the transition? One of the principal reasons for this difficulty was the purely formal definition of the concepts of time and space in the matrix theory, which bore no relation to evolution over time in a physical system. Pauli had mentioned this fact as early as November 1925 in a letter to Bohr. Cornelius Lanczos later argued that an atom in the matrix approach is a timeless entity (1926, 815).8 Heisenberg agreed that the concept of time has no more the usual meaning in the new theory than the concept of space-both are merely formal symbolic artifacts. 6. "In the further development of the theory, an important task will lie ... in the manner in which symbolic quantum geometry goes over into vLc;ualizable classical geometry" (Bom. Heisenberg, and Jordan 1926, 322). 7. "The worst is that it does not become clear to me how the transition into classical theory takes place" (Heisenberg to Pauli, 23 October 1925, PC, 251). 8. Although the matrix elements of momentum (p) and position (,,) contain the exponent 27Ti".. t (where i is the square root of -1, ";> is the frequency associated with the transition from state i to state k, and t is time), nothing changes in the calculations if one Simply writes exp(27Til''')' without dependence on time. Actually, Lanczos notes, in a consistent discontinuous theory there is no place for such a continuous parameter, and indeed the dependence of the matrix elements on time is never used. Differentiation with respect to time is introduced into the theory only in order to preserve the formal analogy with the Hamiltonian equations of classical mechanics: the differentiation of matrix " with respect to t gives the result dqldt = (21ri/h)(Wq - qW), where W is the energy malrix and h Planck's constant. This formula indicates a purely algebraic relation between matrices, rather than an evolution in time. Pauli presented similar arguments in his letter to Bohr and speculated that perhaps time could be defined through the concept of energy (pauli to Bohr, 17 November 1925, PC, 260).

22

Chapter Two

The meaninglessness of the concept of space-time in the original version of the matrix theory had momentous consequences. Carried to a logical conclusion, it meant eliminating the concept of a particle, or "thinghood," from the atomic domain. The original matrix program precluded not only a probabilistic interpretation (which presupposed that an electron does indeed occupy a definite position in space and provided formulas for estimating that position's probability) but the type of physical interpretation Heisenberg gave later in his paper on uncertainty relations (Heisenberg 1927b). To doubt the existence of the position of the electron in time, as the original theory did, is more radical than to question the existence of simultaneous position and velocity. Heisenberg's uncertainty interpretation does not limit infinite precision of position when momentum remains undetermined: it was a visualizable (anschauliche) interpretation of microphysics, although Heisenberg had previously asserted that such a visualizable interpretation was impossible. In order to understand how this change occurred, we need to take into account the overwhelming success of Schrodinger's theory and the vehement confrontation that developed between Schrodinger and Gottingen.

Was the Original Matrix Theory a Theory of Particles? The concept of particles was hardly compatible with the original matrix approach. The relations between the matrices q, p, and the like were defined formally so as to retain the Hamiltonian formalism and the analogy with classical mechanics. The matrix theorists considered the positions of electrons themselves to be unobservable: only the frequency, intensity, and polarization of the emitted radiation can be measured. As Born announced, "We therefore take from now on the point of view that the elementary waves are the primary data for the description of atomic processes; all other quantities are to be derived from them" (1926a, 70).9 In developing matrix mechanics, the GOttingen physicists tacitly 9. Heisenberg himseH pointedly explained the substitution of radiation entities for kinematic entities: In the classical theory the specification of frequency, amplitude and phase of all the light waves emitted by the atom would be fully equivalent to specifying its electron path. Since from the amplitude and phase of an emitted wave the coefficients of the appropriate term in the Fourier expansion of the electron path can be derived without ambiguity, the complete electron path therefore can be derived from a knowledge of all amplitudes and phases. Similarly, in quantum mechanics too, the whole complex of amplitudes and phases of the radiation emitted by the atom can be regarded as a complete description of the atomic system, although its interpretation in the sense of an electron path inducing radiation is impossible. (1933, 292)

Matrix Theory in Flux

23

relied on the "virtual oscillator" model (Bohr, Kramers, and Slater 1924).10 In order to describe interaction between an atom and radiation in close analogy with classical theory, the authors replaced the atom with a set of "virtual" oscillators whose frequencies corresponded to frequencies of transitions between the stationary states of the atom. They held that in each stationary state the atom continuously radiates "virtual" waves whose frequencies correspond to the possible transitions from this state to all others. The authors attempted to reinterpret from a wave theoretical standpoint all the phenomena successfully explained by light quanta. Thus Bohr, Kramers, and Slater explained the Compton effect, in which X-rays scatter and change frequency upon impact with matter, by ascribing the change in frequency to the Doppler effect. This explanation required them to assume that the center of the waves emitted by the electron did not coincide with its kinematic movement. We have here the first intimation of how incompatible a wave theoretical description is with regular kinematics. In 1925 Heisenberg joined Kramers in a paper that dealt with the dispersion of radiation by atoms and spelled out, in a rigorous mathematical way, the ideas only roughly outlined in the presentation of Bohr, Kramers, and Slater. The authors further pursued the program of eliminating light quanta from physics. The same kinematic curiosity appeared as in the paper by Bohr, Kramers, and Slater, on which it was based: the center of the waves emitted by the atom moved relative to the excited atom (Kramers and Heisenberg 1925). Faced with this incompatibility between kinematics and the wave theory, the Gottingen-Copenhagen physicists chose the wave theory. Born, lecturing at MIT in the winter of 1925-26, argued that explanations of the Compton effect assuming that light quanta and electrons are corpuscular were less fruitful than explanations relying on the wave approach through the Doppler effect. Calculations showed that the directions of motion of the electron and the wave center did not coincide: "We therefore stand before a new fact which forces us to decide whether the electronic motion or the wave shall be looked upon as the primary act." Because "all theories which postulate the motion have proved unsatisfactory," Born opted for the description based on elementary waves (1926a, 70). Heisenberg gradually realized how basic is the incompatibility between the usual kinematics and the wave theory of light. Even for a hydrogen atom (a case of one-particle periodic motion), according to 10. Slater's original conception involved light quanta guided by a "virtual" field; Bohr and Kramers disposed of the light quanta. For a discussion of Bohr's opposition to Einstein's idea of light quanta and its influence on the Bohr-Kramers-Slater theory, see Klein (1970).

24

Chapter Two

the wave theory one should obtain equidistant spectral lines, and not lines merging into a continuous limit series (Heisenberg 1926b, 990).u One could adhere either to ordinary kinematics or to the wave theory, but not to both; the recurrent confrontation with kinematic peculiarities made Heisenberg fully aware of the need to choose between the usual kinematics and the wave theory. Heisenberg chose the latter and reinterpreted kinematics in such a way that it would lead to the correct spectral, and not the orbital, frequencies of the emitted waves. This account suggests that the elimination of unobservables was invoked ex post facto-as justification and not as a guiding principle-a point I will elaborate on in chapter 3. The following statement by Heisenberg supports this conclusion: "One could circumvent this difficulty only by giving up altogether the assignment to the electron or to the atom of a definite point in space as a function in time; for justification one had to assume that such a point also cannot be directly observable" (1926b, 990, my italics). The Gottingen physicists regarded the virtual oscillator model as more than a heuristic device. For Born. virtual oscillators were "the real primary thing," and the interaction of electrons in the atom" consists of a mutual influence (irradiation) exerted by virtual resonators on each other" (1924, 190). Heisenberg assumed that "something in the atom must vibrate with the right frequency" (Heisenberg to van der Waerden, 8 October 1963, van der Waerden 1967, 29). Pauli (1926b) described an atom at the time as a collection of harmonic partial vibrations, associated with transitions between different stationary states, and not as a constellation of particles tied kinematically to the occupation of certain stationary states. These vibrations cannot be combined into" orbits." 12 As Heisenberg put it, "In quantum theory it has not been possible to associate the electron with a point in space.... However, even in quantum theory it is possible to ascribe to an electron the emission of radiation" (1925,263). Thus the original matrix theory was saturated with wave theoretical concepts. Originally, matrix mechanics was a symbolic algebraic theory, and the only concepts connected to the physical situation were wave 11. This is what Heisenberg meant by the remark at the beginning of his reinterpretation paper that" the Einstein-Bollr frequency condition ... already represents such a complete departure from classical mechanics, or rather (using the viewpoint of wave theory) from the kinematics underlying this mechanics, that ... the validity of classical mechanics simply cannot be maintained" (1925, 261-62). 12. Moreover, virtual oscillators, as opposed to classical theory, could not even be looked upon as charged particles. Their "ghostlike" character was revealed by the fact that for emission oscillators the expression (e-)2! m- (where e- is the charge of the virtual oscillators and m- the mass) is a negative number (Kramers 1924).

Matrix Theory in Flux

2S

theoretical (frequency, intensity, and polarization of radiation), not particle kinematic (position in space, or even its probability).

Stationary States and Quantum Jumps Ute matrix theorists justified the existence of stationary states by analogy with waves, very much in the spirit of Schrodinger's explanation in terms of vibrations, which they later rejected vigorously. One result the authors of the Dreimannerarbeit were proud of was that in the matrix theory the assumption that stationary states with certain discrete energies existed was not arbitrary, since their existence followed mathematically from the matrix formalism: "The existence of discrete stationary states is just as natural a feature of the new theory as, say, the existence of discrete vibration frequencies in classical theory" (Born, Heisenberg, and Jordan 1926, 322, my italics). Originally, matrix mechanics and Schrodinger's theory had more in common than is usually appreciated: both considered some vibration process as primary; but whereas Heisenberg reinterpreted classical space-time through these vibrations, Schrodinger left the usual concepts of space-time unchallenged. Schrodinger, indeed, initially regarded his own work as being in the same vein as the matrix approach. Even though their methods differed, "in its tendency, Heisenberg's attempt stands very near the present one," he asserted (Schrodinger 1926b, 30). The authors of the matrix method considered one result of the theory particularly valuable: its ability to obtain discrete solutions without assuming a priori that stationary states existed as Bohr had. Heisenberg was especially proud of the independence of the new quantum mechanics from this assumption. The theory is instead derived solely from the commutation relation pq - qp = (h/21ri)1 (Heisenberg to Pauli, 18 September 1925, PC). The stationary states in the matrix approach were purely formal artifacts, characterized by the numbers n (or n" ... , nf in the case off degrees of freedom), which were associated with the definite values of energy and perhaps of angular momentum. Besides this, it was not clear whether the states could be given any phYSical interpretation at all, because they were all "interlocked" by the formalism in such a way that one could not assign a varying physical magnitude to a given stationary state (Dirac 1925). Stationary states in the new theory were different from the original conception. 13 In the old theory the sequence of stationary states was that 13. The authors of the Dreimannerarbeit stated this clearly when discussing the solution of the hannonic oscillator in the new theory. They argued that nothing changes physically if the sequence of quantum numbers 0, 1, 2. 3, ... is rearranged into a new sequence nUl nt, n", n" ... such that certain formulas stilJ hold.

26

Chapter Two

of increasing values of energy, and this order had a fundamental physical significance (of merging continuously into a classical limit). This was not the case in the new theory. liThe new mechanics presents itself as an essentially discontinuous theory in that herein there is no question of a sequence of quantum states defined by the physical process, but rather of quantum numbers which are indeed no more than distinguishing indices which can be ordered and normalized according to any practical standpoint whatsoever" (Born and Jordan 1925a, 300-301). The matrix theorists realized that the theory's inability to incorporate the concept of the state of the system was a serious drawback. It was clear that an atomic system can exist in certain states for definite amounts of time; therefore, a theoretical description of such states was needed. The ability of Schrodinger's theory to give a straightforward definition of a stationary state through a wave function was one of its advantages, as Hendrik Lorentz pointed out in a discussion of the comparative merits of the two theories (Lorentz to Schrodinger, 27 May 1926, Przibram 1967, 44), and as Bohr argued later in the Como lecture (see chapter 6). That superiority originally disposed Born also to regard wave mechanics as physically more significant than the matrix approach. In order to counter Schrodinger, the Gottingen theorists needed a matrix interpretation of the quantum state. The only way available at the time was to resuscitate Bohr's original concepts of stationary states and jumping electrons. Heisenberg collaborated fully with Bohr for this purpose. As he admitted years later: "It was extremely important for the interpretation to say that the eigenvalues of the Schrodinger equation are not only frequencies-they are actually energies. In this way of course one came back to the idea of quantum jumps from one stationary state to the other.... But even when we knew this and accepted the quantum jumps, we did not know what the word 'state' could mean" (1973,269). Schrodinger was desperate about the reintroduction of "these damned quantum jumps" (quoted in Heisenberg 1967, 103). This weird concept seemed alien not only to his theory but to the matrix approach, Originally constructed to dispense with such illustrative notions.

Matrix Mechanics and Determinism In their recollections, the founders of quantum mechanics described their efforts to construct the new quantum mechanics as guided by a belief in indeterminism. Historians and philosophers of science often follow this lead, seeking the sources of such beliefs in the cultural milieu (Jammer 1966; Forman 1971). Yet we find no strong opinions expressed on the issue of causality during the creative stages of the erection of the new theory. Nor was the new matrix theory initially inter-

Matrix Theory in Flux

27

preted in an indeterministic fashion. Instead, matrix mechanics was viewed as a discrete deterministic theory. In this approach the problem was fully detennined when the Hamiltonian of the system was known. By a principal axis transformation that diagonalized the matrix H, in principle one obtained the energy values and the matrices p and q. Matrix mechanics was constructed by analogy to be "as close to that of classical theory as could reasonably be hoped" (Born, Heisenberg, Jordan 1926, 322). What about the fact that the matrix elements represented transition probabilities? The Gottingen theorists made no categorical indeterministic deductions from it; rather they simply did not exclude the possibility that this was a temporary weakness of the theory, very much the conclusion Einstein had reached about transition probabilities in his quantum theory of radiation in 1917 (Einstein 1917, 76). Pauli, for example, considered that the inability of the matrix theory to detennine exactly when a transition occurs was a weakness: the time of emission of the photoelectron is definitely observable, and so a satisfactory physical theory should be able to calculate it. A satisfactory physical theory should contain no probability concepts in its fundamental propositions. Pauli was prepared to "pay a high price" to eliminate these probabilities (Pauli to Bohr, 17 November 1925, PC, 260). Heisenberg, under Pauli's influence, also considered this question in a letter to Einstein. Should the times of transition be regarded as observable, and would matrix mechanics be able to detennine them? The matrix theory was still in such an incomplete (unfertig) stage, complained Heisenberg, that he simply did not know what stand to take on these questions (Heisenberg to Einstein, 30 November 1925, Einstein Archive, Hebrew University of Jerusalem). In accordance with his emphasis on using observable electromagnetic variables, Heisenberg (1926b) presented matrix elements as "radiation magnitudes" (Strahlungsgrossen), and not as transition probabilities, in his Naturwissenschaften paper. He seemed originally to suppress the statistical meaning of matrix elements, expressing his pleasure that certain relations formerly deduced from statistical considerations (frequencies of transitions) could be deduced solely by the mathematical manipulation of "radiation-value tables" (matrices; 1926b, 990). Heisenberg was nonetheless open to the possibility that for certain questions quantum theory might not go beyond statistical answers. Einstein himself was not sure whether a deterministic account of microscopic phenomena would be possible, or whether there would always remain a statistical residue (Einstein to Born, 27 January 1920, Born 1971). The answer was unclear to the majority of physicists. The use of statistical methods is not, of course, in itself evidence of a desire to dispose of causality; it is rather a sign that, at least for the time being, statistical methods yield

28

Chapter Two

the best scientific results. Heisenberg's preference for indeterminism evolved gradually in complex theoretical and human dialogical contexts (see chapters 4, 5, 9, and 10).

Mathematical Difficulties of the Matrix Approach The matrix method of solving quantum mechanical problems was formulated in an astonishingly simple and general way. For any pair of values po, qo that satisfies the basic commutation relation pq - qp = (h/27Ti)1 (as, for example, in the simple case of the harmonic oscillator), solving the quantum problem (the problem of integrating the canonical equations for the given H(Pq» reduces to determining a matrix 5 that diagonalizes the Hamiltonian: H(pq) = 5H(Poqo)5- 1 = W, where Wis a diagonal matrix. 5 then gives the solution of the canonical equations p = 5p o5- 1 and q = 5q o5- 1• The simplicity of this economical and beautiful formulation was, however, quite misleading: it was practically useless because of the difficulty of calculating the reciprocal matrix 5- 1 . Matrix mechanics could not solve any general case, only, by perturbation methods, those physical problems that could be considered approximations to solved cases. The application of perturbation methods presupposed "that several specially simple systems which are used as starting points in calculus are completely known" (Born 1926a, 99; see also London 1926). The key word here is "completely": the "interconnectedness" of the quantum system in the matrix approach was such that one had to know both the frequencies and the intensities of the unperturbed system in order to calculate any of them for the perturbed system. The crucial test of the theory was whether it could solve the central problem of the atomic domain-the hydrogen atom. No wonder Heisenberg rejoiced when Pauli succeeded in working out the Balmer formula for the hydrogen spectrum, though Pauli did so with difficulty and at the price of additional assumptions (Pauli 1926a; Heisenberg to Pauli, 3 November 1925, PC). P. A. M. Dirac and Gregor Wentzel also obtained the solution of the hydrogen atom, a success for the matrix approach, but not the grand triumph generally assumed (Dirac 1925, 1926; Wentzel 1926a). In order to proceed from the simple hydrogen atom to more complicated atomic systems by perturbation methods, one needed to know both the frequencies and the intensities of radiation of the hydrogen atom; but Pauli, Dirac, and Wentzel all failed to calculate the intensities. Moreover, it seemed hopeless to obtain this solution by matrix methods. 14 Matrix mechanics was thus at an 14. This opinion is expressed by Jordan: "It appeared hopeless to calculate the matrix elements" (1927a, 641).

Matrix Theory in Flux

29

impasse: the solution of the hydrogen atom could not lead to any further advance of the theory, and consequently the perturbation methods discussed in the Dreimannerarbeit were useless for new physical applications. This serious drawback was duly noted, by Fritz London. for example (London 1926, 921). The authors of matrix mechanics found themselves in an ironic position. They had erected the new quantum theory primarily in order to approach multiple-electron systems, where the old methods had already failed. Yet the mathematical difficulties of matrix mechanics virtually prohibited its extension beyond simple systems with one moving particle. In fact, it was only after SchrOdinger's wave mechanics had appeared that Pauli succeeded in calculating the intensities of the Balmer terms, and only by using Schrodinger's eigenfunctions of the hydrogen atom for his solution (Pauli to Lande, 2 June 1926, PC, 327). The superiority of Schrodinger's solution of the hydrogen atom over those of Pauli, Dirac, and Wentzel showed the clear advantage of his theory for solving quantum systems in central fields. Dirac's and Wentzel's calculations did not determine whether the quantum numbers of Balmer energy terms were integers or half-integers, while Schrodinger's calculations resulted unambiguously in half-integers. Both Dirac and Wentzel, and later Heisenberg and Jordan, used a two-dimensional treatment instead of the correct, three-dimensional one (Schrodinger to Lorentz, 6 June 1926, Przibram 1967, 64 -65; Heisenberg and Jordan 1926).15 They reached agreement with the experimental results by tailoring questionable methods to results known in advance: if they had conducted the calculations rigorously, they would have obtained the wrong answer, as Schrodinger suspected and John van Vleck (1973) has since demonstrated. Dirac himself used Schrodinger's solution in The Principles of Quantum Mechanics (Dirac 1930), and Pauli scolded Born and Jordan for including his own complicated solution, inferior to SchrOdinger's, in their book Elementare Quantenmechanik (Born and Jordan 1930). There were other substantial mathematical difficulties as well, including the problem of coordinates (for a full discussion. see Beller 1983). The matrix approach nevertheless showed promise. It seemed especially well suited to calculations involving angular momentum matrices. Consequently, it allowed straightforward quantization of the angular momentum components (that is, the calculation of magnetic quantum numbers) and the deduction of selection rules without extraneous assumptions (unlike the old quantum theory, where certain orbits, leading to collision between electrons and the nucleus, were excluded). It 15. Schrodinger initially obtained half-integers, not integers, because spin was not yet taken into account.

30

Chapter Two

also enabled the intensities in the normal Zeeman effect and the Stark effect to be calculated (Born 1926a; Born, Heisenberg, and Jordan 1926). Moreover, matrix mechanics successfully treated the harmonic and anharmonic oscillators, dispersion, and, though incompletely, the hydrogenatom. The Emotional Confrontation between the Matrix Physicists and Schrodinger The successes of the matrix mechanical method were modest compared with the difficulties encountered. Most of the problems treated using the matrix approach had been solved previously. Their solution was therefore more an encouraging sign of the new theory's possible validity than a guarantee of future success. The most outstanding atomic problems-hydrogen intensities and helium energy terms-awaited solution. They proved to be as resistant to the matrix approach as to the old Bohr-Sommerfeld theory. Even those who favored the matrix approach were reluctant to use it. Thus Arnold Sommerfeld declared: "There was clearly an element of truth in it [matrix mechanics], but its handling is frighteningly abstract" (1927, 231). There were also grave problems of physical interpretation. "Heisenberg's theory in its present form is not capable of any physical interpretation at all" was the harsh verdict (Campbell 1926, 1115). There was simply no space-time" gravy," to use Hermann Weyl's characterization, in the matrix representation (Sommerfeld 1927, 231). The elimination of unobservables led to the elimination of space-time and of physical reality itself, including the by then familiar electrons. The extreme Machean approach, which eliminated everything but immediate sense perception (intensities, frequencies, and polarization of spectral lines) and a highly abstract uninterpreted formalism, did not seem tenable. Einstein questioned the soundness of it, and London (1926) and Nicholas Rashevsky (1926) argued that it was inconsistent. The ability to understand the transition from the micro- to the macrodomain was questioned. Nor could the matrix approach initially be reconciled with the definition of a quantum state. The lack of visualizability was a heuristic, if not a conceptual, hindrance. To build a truly discontinuous theory, one had to proceed with no suitably developed mathematics and in a virtually complete conceptual vacuum. After the emergence of Schr6dinger's theory, it is no wonder the approach was abandoned, first by Born (who proposed the probabilistic interpretation), then by Pauli (who extended Born's approach), and later by Heisenberg (who advanced an interpretation of the indeterminacy relations). No wonder, too, that the creators of the new mechanics did not seem to have much confidence in their theory in the beginning. Heisenberg's

Matrix Theory in Flux

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changing moods in the fall of 1925 reflected his doubts about the new theory. Thus, in a letter to Pauli, Heisenberg wrote that he considered the principal axis transformation the most important part of the whole theory (Heisenberg to Pauli, 23 October 1925, PC), only to call it "formal rubbish" three weeks later (Heisenberg to Pauli, 16 November 1925, PC). Heisenberg's letters to Dirac and Einstein at the time do not reflect a belief in the validity of the matrix approach. "I read your beautiful work with great interest," he wrote to Dirac. "There can be no doubt that all your results are correct, insofar as one believes in the new theory" (quoted in Dirac 1977, 124, my italics).16 Nor do the original published versions of matrix mechanics convey any feeling of an extraordinary scientific breakthrough. A cautious tone is adopted in the Dreimannerarbeit: even though the authors would like to conclude that the theory might be the correct one because of its mathematical simplicity and unity, they realize nonetheless that it is yet unable to solve the crucial problems of the quantum domain (Born, Heisenberg, and Jordan 1926). Even less optimistic are Born's concluding remarks in his MIT lectures: "Only a further extension of the theory, which in all likelihood will be very laborious, will show whether the principles given above are really sufficient to explain atomic structure. Even if we are inclined to put faith in this possibility, it must be remembered that this is only the first step towards the solution of the riddles of the quantum theory" (Born 1926a, 128). It is not surprising, therefore, that except for the inventors of the new theory and those under their direct influence, only a very few physicists attempted to employ the matrix method. Most physicists, it seems, decided to "wait and see"-they would not submit to studying complicated mathematical techniques until the new theory proved its worth. Nor were they inclined to direct their students to study matrix mechanics. Felix Bloch, Peter Debye's student, was not even aware of the matrix theory before he learned about it from Schrodinger's publication. 17 Even the biggest success of the matrix approach-the solution of the Balmer terms for the hydrogen atom-lacked both the completeness and the elegance one would expect from a full-fledged theory. Pauli himself was pointing to the limitations of the matrix approach when later referring to his own result as having been derived by an "inconvenient and indirect method" (1932, 602). In contrast, Schrodinger's theory, mathematically powerful and 16. Heisenberg's insecure and self-critical mood obviously persisted after Pauli's solution of the hydrogen spectrum, which, according to the usual historical accounts, dispelled any doubts about the correctness of the new theory. 17. As he wrote years later: "I did not learn about the matrix fonnulation of quantum mechanics by Heisenberg. Born and Jordan until I read that paper of Schrodinger, in which he showed the two fonnulations to lead to the same results" (Bloch 1976,24).

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Chapter Two

familiar (as well as physically more accessible), was hailed by the community of theoretical physicists. "It was the most astonishing among all the astonishing discoveries of the 20th century," declared Sommerfeld (quoted in Moore 1989, 2). It is a historical myth that the enthusiasm was limited to the conservative part of the scientific community. It was welcomed, for example, by such unconventional minds as Charles Darwin, Fritz London, and Enrico Fermi. The success of Schrodinger's theory contributed, in an indirect way, to the dissemination of the matrix approach. Many physicists learned about the existence of matrix mechanics from Schrodinger's publications. The proof of the equivalence of matrix and wave mechanics endowed the unfamiliar and abstract matrix approach with credibility.18 Yet the young matrix theorists reacted to Schrodinger's theory with disbelief and hostility (except for Born; see the next section of this chapter). Heisenberg hoped initially that Schrodinger's theory was wrong. Years later Heisenberg explained that he deliberately ignored wave mechanics before Schrodinger's equivalence paper because of the interpretation Schrodinger attached to it (interview with Heisenberg, AHQP). This explanation is not convincing. SchrOdinger's initial presentation of his theory was undertaken in "neutral mathematical form" (Schrodinger 1926a, 9). Schrodinger's opinion about the need "to connect the function", with some vibration process in the atom, which would more nearly approach reality than the electronic orbits, the real existence of which is being very much questioned to-day" (1926a, 9), did not contradict the original inspiration behind Heisenberg's reinterpretation paper. Heisenberg also doubted the reality of electron orbits and tried to detect those internal vibrations that produce radiation in agreement with experiments. There was no substantial reason for Heisenberg's aversion to Schrodinger's theory; indeed, Schrodinger believed initially that his and Heisenberg's work in their "tendency" were very close.19 Heisenberg's hostility to Schrodinger's theory seems more likely to be connected with his instinctive reluctance to admit anybody else into territory that the ambitious Heisenberg considered his own. This probably was also the reason for Dirac's initial opposition to Schro.. dinger's theory. As Dirac reported later, he ignored SchrOdinger's theory 18. Lorentz wrote to SchrOdinger: "I was particularly pleased with the way in which you ... construct the appropriate matrices and show that these satisfy the equations of motion. This dispels a misgiving that works of Heisenberg, Born and Jordan ... inspired in me" (Przibram 1967, 43). 19. The hint about a possible "beat" wave model could have aroused Heisenberg's objection because he no longer inclined toward building visuaJizable realistic models. Yet the interpretive issues in SchrOdinger's first paper were so peripheral and understated that it would have been more natural to overlook them instead of the advance SchrOdinger had made.

Matrix Theory in Flux

33

in the beginning because there already was one quantum mechanics, so no other was needed. Dirac admitted that "he definitely had a hostility to SchrOdinger's ideas to begin with, which persisted for quite a while" (1977, 131). Pauli also reacted to Schrodinger's ideas with suspicion-he considered Schrodinger's approach verriict (crazy, foolish; Pauli to Sommerfeld, 9 February 1926, PC). Learning of Sommerfeld's regard for Schr6dinger's work, however, Pauli took a closer look at it, decided that it belonged among the "most meaningful" recent publications, proved the equivalence between matrix mechanics and wave mechanics, and subsequently strove to elucidate its physical meaning by trying to understand the connection between Schrodinger's formalism and Einsteinde Broglie waves (Pauli to Jordan, 12 April 1926, PC). Heisenberg, who could no longer contend after the equivalence proof that Schrodinger's theory was wrong, declared that its only value was its ability to calculate the matrix elements (Heisenberg to Pauli, 8 June 1926, PC). Jordan (1927a) arrived at a similar conclusion: the "meaning of the thing" was clear-eigenfunctions merely provided a new mathematical method for solving the equations of matrix mechanics. Jordan became one of the most militant opponents of Schrodinger's interpretive efforts. Schrodinger should have been satisfied with the mathematical advance and should not have even attempted anything more than a mathematical elaboration, declared Jordan (1927a, 615). The new theory must be "interpreted physically in close analogy with the older notions of stationary states and quantum jumps, and with Heisenberg's theory" (1927b, 567). In a review of Schrodinger's collected papers on wave mechanics, Jordan declared Schrodinger's theory to be devoid of any physical meaning and stated (incorrectly) that such was the opinion prevailing among the majority of physicists (Jordan 1927d). A novice in the field should not be exposed to Schrodinger's work without prior appropriate instruction in physical matters in the GottingenCopenhagen spirit, Jordan continued. Schrodinger, understandably, was outraged, and he complained about this review to Born (Schrodinger to Born, 6 May 1927, AHQP). Born admitted that Jordan somewhat exceeded his limits and blamed it on jordan's youthful temperament (Born to Schrodinger, 16 May 1927, AHQP). Schrodinger's hope that his theory would have a self-sufficient physical interpretation was not unreasonable. This expectation was consistent with the belief of physicists from Galileo to Einstein, that mathematical simplicity and power are unmistakable signs of a theory's physical significance. 20 Schrodinger attempted initially to elucidate some 20. SchrOdinger undoubtedly expressed the feelings of many physicists when he pointed to the conceptual hindrance implied by the elimination of intuitive space-time

34

Chapter Two

"conceivable mechanism" by which microphenomena take place in regular space-time. Physical reality, according to Schrodinger's early attempts at interpretation, was akin to the reality of classical electrodynamics-smeared clouds of electron matter (wave packets) obey wave mechanical equations. This ontology soon proved to be abortive; yet the "intuitiveness" of Schrodinger's approach was not confined to its ability to provide (or not) classical idealized space-time models. Rather, the physical significance of Schrodinger's theory lay in its ability to provide some qualitative handle on the essential aspects of the microworld. Schrodinger's theory deciphered the mystery of quantization; it explained why atoms in stationary states do not radiate. Despite the officialline that denied physical Significance to Schrodinger's theory, the matrix physicists, even Jordan, could not help but sometimes praise Schrodinger for just these assets. 2 ' Heisenberg understood early that there must be some very close connection between Schrodinger's approach and his own. He realized that it was Schrodinger's theory that might prove helpful in elucidating the physical meaning of his own abstract version of quantum mechanics. After Schrodinger's first paper appeared, Heisenberg wrote to Dirac: "A few weeks ago an article by Schrodinger appeared ... whose contents to my mind should be closely connected with quantum mechanics. Have you considered how far Schrodinger's treatment of the hydrogen atom is connected with the quantum mechanical one? This mathematical problem interests me especially because ... one can win from it a great deal for the physical significance of the theory (Heisenberg to Dirac, 9 April 1926, AHQP, my italics). Pauli agreed, citing the possibility of "look[ing] at the problem from two different sides" (Pauli to Heisenberg, 12 April 1926, PC). Heisenberg fully exploited the interpretive possibilities opened by the wave theory, using Schrodinger's imagery, which he publicly pictures in matrix mechanics. The problems that atomic physics had to treat theoretically were presented, SchrOdinger pointed out, in "an eminently intuitive form; as, for example, how two colliding atoms or molecules rebound from one another, or how an electron or a-particle is diverted when it is shot through an atom with a given velocity and with the initial path at a given perpendicular distance from the nucleus." How is one even to begin to treat such problems if one operates only with such abstract ideas as transition probabilities, energy levels, and the like? Darwin's words that "the ultimate theory will be one of space and time again" echoed Schrodinger's hopes (Darwin to Bohr, 1928, AHQP). 21. Jordan noted that Schrodinger's demystification of quantization (quantization follows from the condition of finitude and one-vaIuedness of wave amplitude) was more akin to "our physical understanding" than quantization imposed a priori. Born explained why there is no radiation in stationary states by using SchrOdinger's wave function (Born 1969,148).

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35

denounced, as a rich source of suggestions for constructing a rival interpretation. Heisenberg's elaboration of the uncertainty relations hinged on a translation of a "wave packet ala Schrodinger" (Heisenberg to Pauli, 23 February 1927, PC) into the language of a particle ontology (see the detailed discussion in chapter 4). Bohr understood clearly that the wave theory played an essential role in Heisenberg's considerations, both historically and philosophically.22 Bohr himself strove to elucidate the physical significance of Schrodinger's wave theory in his Como lecture (see chapter 6). Like the majority of the scientific community (the alleged "conservatives") he preferred the intuitiveness of Schrodinger's version to the formal abstraction of the matrix theory: "This ingenious attack [the matrix approach] upon the problem of the quantum theory makes, however, great demands on our power of abstraction, and the discovery of new artifices [wave mechanics] which, in spite of their formal character, more closely meet our demands for visualization, has therefore been of profound significance in the development and clarification of quantum mechanics" (Bohr 1929a, 110-11).23 Nor is the emergence of the Gottingen-Copenhagen statistical ontol-

ogy in particle terms comprehensible without taking into consideration the selective borrowing of Schrodinger's interpretive ideas and their translation into particle language. Born's statistical interpretation was, to a large degree, a translation into particle language of Schrodinger's idea that the !/I-function determines the electron charge density; Pauli fused Schrodinger's idea of a "weight function" with Born's interpretation, arriving at the interpretation of the wave function as giving the probability that the system is in a specific configuration. Dirac similarly used the suggestiveness of Schrodinger's conceptions in forming his probabilistic ideas. 24 22. Heisenberg wrote to Dirac about his confrontation with Bohr over the uncertainty paper: "Prof. Bohr says, that one in all those examples sees the very important role, which the wave-theory plays in my theory and, of course, he is quite right" (Heisenberg to Dirac, 27 April 1927, AHQP). 23. Bohr expressed similar reservations about the mathematical complexity of matrix mechanics and maintained his preference for the wave mechanical version throughout his life. In 1938 he wrote: "On account of the intricate mathematical operations involved, it was, however, of utmost importance, not only for the practical use of the formalism. but even for the elucidation of essential aspects of its consequences, that the treatment of any quantum-mechanical problem could be shown to be essentially reducible to the s0lution of a linear differential equation" (Bohr 1939, 387). 24. "5chrOdinger's wave representation of quantum mechanics has provided new ways of obtaining physical results from the theory based on the assumption that the square of the amplitude of the wave function can in certain cases be interpreted as probability" (Dirac 1927, 621).

36

Chapter Two

From a purely conceptual point of view, the intense hostility to Schrodinger's ideas (rather than, say, polite disagreement) is puzzling. 25 Partly, as I have noted, the matrix theorists resented Schrodinger's intrusion into their "territory." It did not seem feasible that an outsider could arrive at the long-sought solution of the quantum riddle, and that the solution could be that simple. Schrodinger's success aroused both disbelief and envy. The assessment by Heisenberg that it was "too good to be true" reveals this attitude (1971, 72). So does Born's dismissal: "It would have been beautiful if you [Schrodinger] were right. Something that beautiful happens, unfortunately, seldom in this world" (Born to Schrodinger, 6 November 1926, AHQP). Yet disbelief and envy, strong as these feelings are, were only a part of the psychosocial setting in which the new quantum mechanics was erected. The Gottingen-Copenhagen physicists saw in Schrodinger's program something capable of extinguishing the matrix approach (interview with Jordan, AHQP). Had Schrodinger succeeded in giving a satisfactory interpretation without the Gottingen-Copenhagen concepts, he might have eliminated the need for the matrix approach altogether, in view of the mathematical equivalence of the matrix and wave theories and the greater manageability and familiarity of the latter. Many physicists found Schrodinger's theory much more attractive and were inclined to regard Schrodinger's physical approach as the more correct of the two candidates (interview with Jordan, AHPQ). A flood of papers, most following Schrodinger and ignoring the matrix approach, highlighted the reality of the threat. Schrodinger's theory was successfully applied to a great variety of problems unamenable to matrix treatment. Born recalled the successes of Schrodinger's mechanics: "In the meantime, Schrodinger's wave mechanics appeared, and won the approbation of theoretical physicists to such an extent that our own matrix method was completely pushed into the background, particularly after Schrodinger himself had shown the mathematical equivalence of wave and matrix mechanics" (1971, 104). Expressing himself more strongly, Born said during an interview with Thomas Kuhn: "Wave mechanics was considered the real quantum mechanics by everybody, while matrix theory was completely neglected" (interview with Born, AHQP).26 Born was indeed unhappy at the time about the "world-wide victory" of wave mechanics (Schrodinger to Born, 17 May 1926, AHQP). This "victory," as Heisenberg clearly understood, was pregnant with 25. Heisenberg used such emotionally charged words as abscheulich (repelling. disgusting) in characterizing Schrodinger's approach. The connection between anecdotal and conceptual history, and the fonnative role of emotions in cognitive endeavors, is analyzed in Beller (l996b). 26. Citation analysis confirms Born's judgment (Kojevnikov and Novik 1989).

Matrix Theory in Flux

37

far-reaching consequences. It implied no less than the power to "influence ... the research of the following century" (1952, 60). The "victory" in Bohr's and Sch.rodinger's characterization similarly meant "to realize one's wishes for the future of physics." 27 The weight of the threat to the Gottingen-Copenhagen version of physics was revealed at the Munich conference held at the end of summer 1926. Most participants there aligned themselves not only with Sch.rodinger's methods but also with his interpretive aspirations. Even Sommerfeld, or so it seemed to Heisenberg, succumbed to the persuasive force of Sch.rodinger's mathematics.28 Heisenberg'S critique of Sch.rodinger's intentions "failed to impress anyone," and Wilhelm Wien crowed to the despairing Heisenberg that his version of quantum mechanics with the nonsensical quantum jumping was" finished" (Heisenberg 1971). Heisenberg immediately reported this alarming situation in a letter to Bohr, and Schrodinger was subsequently invited to Copenhagen for what would become heated discussions. 29 After Sch.rodinger left Copenhagen, a feverish hunt for an adequate interpretation occupied both Heisenberg and Bohr. The emerging Gottingen-Copenhagen interpretation did not weaken the "victory" of Schrodinger's methods. Even physicists who had made some initial contributions to the matrix approach turned to the wave theory with relief, Wentzel and London among them. Results obtained in the matrix framework were often translated into wave language, as, for example, William Gordon's wave treatment of the Compton effect, which came after Dirac's work in the matrix framework. Such duplication of scientific results was justified by the argument that "Schrodinger's methods possess the advantage of using the familiar mathematical forms only" (Gordon 1927, 117). When Born tried to show that some results achieved in the wave framework could also be easily obtained by matrix methods, Paul Ehrenfest called the latter" a bad habit" (interview with Oskar Klein, AHQP). Matrix tools could not 27. SchrOdinger to Bohr, 23 October 1926, AHQP; reprinted in Bew; 6:459-61, translation on 12. 28. Sommerfeld did have some reservations but apparently abstained from expressing them. Sommerfeld reported to Pauli about the Munich conference in a letter: " 'Wave mechanics' is an admirable micromechanics, yet it is still far off from solving the fundamental quantum riddle" (Sommerfeld to Pauli, 26 July 1926, PC). 29. Heisenberg's desoiption of these discussions is among the most quoted passages in the literature of the history of quantum theory. Heisenberg's tale is highly dramatic: "Though Bohr was an unusually considerate and obliging person, he was able in such a discussion. which concerned epistemological problems which he considered to be of vital importance, to insist fanatically and with almost terrifying relentlessness on complete clarity in all arguments.... He would not give up, even after hours of struggling.... It was perhaps from over-exertion that after a few days Schrooinger became ill and had to lie abed as a guest in Bohr's home. Even here it was hard to get Bohr away from Schro.. dinger's bed" (1967, 103).

38

Chapter Two

compete with wave mechanical ones. By 1929 lithe research was dominated by wave mechanics, and matrix mechanics so to speak only came back through group theoretical arguments" (interview with Hendrik Casimir, AHQP). Born and Jordan made a last, desperate attempt to oppose this trend: they wrote a book-Elementary Quantum Mechanics (1930)-relying solely on matrix methods, in which Schrodinger's wave function did not appear even once. This book "in view of the general predisposition in favor of Schrodinger ... was not favorably received" (interview with Born, AHQP). Pauli (1932) himself wrote a devastating review: What is the "elementary" quantum mechanics of the present volume? ... Elementary is that quantum mechanics which makes use of elementary tools, and elementary tools are purely algebraic ones; the use of differential equations is ... avoided as much as possible.... Many results of quantum theory can indeed not be derived at all with the elementary methods defined above, while the others can be derived only by inconvenient and indirect methods. Among the latter results belong, for instance, the derivation of the Balmer terms, which is carried out in matrix theory according to an earlier paper of Pauli's dealing with it. In this regard, he will not be able to accuse the reviewer that he finds the grapes to be sour because they hang too high for him. The restriction to algebraic methods also often inhibits insight into the range and the inner logic of the theory.... The setup of the book as far as printing and paper are concerned is splendid. Schrooinger's methods did indeed win an overwhelming victory. But the in terpretation that most physicists seemed to accept was the one given by Schrodinger's opponents. The Gottingen-Copenhagen line was, of course, not unassailable-that critical debates on the philosophy of quantum physics continue to the present day attests most eloquently to this fact. Yet quite apart from the philosophical question of the validity of the opposing approaches, we can ask a sociological question concerning the initial distribution of forces. We will not be surprised to find out who prevailed. At first Schrodinger had the emotional support of many physicists, some distinguished and some not. Yet he struggled with the problems of interpretation virtually alone. Those who identified with his aspirations hardly did anything to advance his efforts. They hoped, as Jordan recalled, that Schrodinger would accomplish his task unaided (interview with Jordan, AHQP). The Gottingen-Copenhagen phYSicists, in contrast, presented a united front. They cooperated intimately, and each contributed extensively to the emergence of the new philosophy. Bohr and Born headed the era's most prestigious schools of theoretical physics, and promising physicists were eager to work with them. Soon Pauli and Heisenberg would

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39

occupy important chairs of their own (Cassidy 1992). Young physicists, who streamed into these centers from allover the world, were exposed automatically to the new philosophy. Because they were more interested in calculating and obtaining definite scientific results than in philosophizing, most of them simply adopted the official interpretation without deep deliberation. Heisenberg was aware of this. In his 1930 book, which he dedicated to the "diffusion of the Copenhagen spirit," Heisenberg conceded that" a physicist more often has a kind of faith in the correctness of the new principles than a clear understanding of them" (1930, preface). The aging Schr6dinger witnessed a remarkable state of affairs: the universal use of his theory coupled with an almost total rejection of his interpretation. Schr6dinger's methods proved indispensable. His philosophy did not. Born's Probabilistic Interpretation: A Case Study of "Concepts in Flux" Born's probabilistic interpretation of the wave function occupies a central place in the philosophy of quantum mechanics. In the orthodox interpretation it signifies the abandonment of determinism and the introduction to a new kind of reality, abstract and "ghostlike." According to Born's reminiscences, his belief in particles rather than waves, together with Einstein's idea of a connection between the intensity of the electromagnetic field and the density of light quanta, made it "almost selfunderstood" to interpret 1I/I1 2 dx as the probability density of particles (Born 1961). However, scholars have expressed some doubts about the authenticity of Born's recollections.3D I have suggested a revision of the history of Born's probabilistic interpretation along the following lines (Beller 1990): 1. Born's probabilistic interpretation was a conceptual contribution that crystallized over a considerable period of time-time during which Born's ideas, as a result of his dialogues with SchrOdinger, Heisenberg, Pauli, and other phYSicists, underwent significant changes. 30. Pais (1982) has noted that if Born had really been stimulated by the analogy of light intensity as a quadratic function and Schrodinger's wave function, he would not have been able, however briefly, to suppose initially that '" rather than 1",1 1 was a measure of probability, as he did in his first collision paper. Stachel (1986) has argued that the source of Born's inspiration was not Einstein's unpublished speculations but rather his work on monatomic gases, in which he suggested a connection between material particles and de Broglie fields. Wessels (1981) has pointed out that in none of Born's original papers on this subject did he interpret 1I/I1 2 dx as a probability of position. These valuable insights found additional reinforcement and explanation in my account (Beller 1990).

40

ChapterTwo

During the formative stage, all of Born's intellectual pronouncements were fluid, ambiguous, and uncommitted. 2. Born's initial contribution-his first collision paper (Born 1926c)was not written, as Born later claimed, in opposition to SchrOdinger's waves. Initially, Born was not involved in any controversy with SchrOdinger at all. In fact, Born was very enthusiastic about SchrOdinger's contribution, including its interpretive possibilities. He appears to have had no strong "belief" in particles; Born was undecided about the wave-particle issue. 3. Born's aim in his first collision paper (Born 1926c) was not to contribute to the clarification of interpretive issues but to solve a particular (yet central) scientific problem. 4. The aim of the collision papers (Born 1926b, 1926c) was not to argue the reality of particles and indispensability of indeterminism, as Born's later recollections would lead us to believe, but rather to describe and theoretically substantiate Bohr's concept of "quantum jumps"-discrete energy changes within an atom during collision processes. Most of the disagreement between Born and Schrodinger, as their correspondence confirms, centered not on the wave-particle dilemma or indetenninism but rather on the existence of these quantum jumps.

5. The probabilistic interpretation of Schrodinger's wave functionthat", gives the probability of position-developed not from the relatively obvious suggestion that", describes the motion of free particles but from the pregnant question of how the wave function is to be interpreted for bound systems. Born's interpretation of 1'" 12 as giving the probabilities of the stationary states of an atom was a crucial contribution, around which the issues of indetenninism and the particlekinematic ontology were elaborated and established. 6. Born's original probabilistic interpretation played a key role in the emergence of the new philosophy of physics not because it was "obviously" correct but because of the ambiguities, difficulties, and paradoxes it raised. The solution to these problems led to the modification of earlier concepts and to the elaboration of new theoretical and philosophical ideas.

Born's probabilistic interpretation can be seen as a "concept in flux" process.31 The uninterpreted mathematical tools left room for ambiguity 31. The term "concept in flux" was used by Elkana (1970) to denote those vague and unspecific ideas that only during the process of simultaneous formation of a theory and its basic concepts become scientifically legitimate. Thus, according to Elkana (1970), in Helmholtz's case the concept of energy and the law of conservation of energy evolved and were clarified as a single process. The dialogical approach of this book indicates that all concepts at the focus of research are in fact "in flux."

Matrix Theory in Flux

41

and permitted freedom from binding epistemological and ontological assumptions. In the development of abstract theoretical physics, it is tools (mathematical or experimental), rather than preconceived metaphysical ideas, that constitute the driving force in the growth of knowledge. And if Born was not committed to particles and indeterminism to begin with, he similarly did not commit himself to wave concepts, despite all his enthusiasm for Schrodinger's theory. Born was instead working in the creative conceptual twilight where "mathematics knows better than our intuition" (interview with Born, AHQP). Born's Collision Papers

The first paper in which Born provided a statistical description of collision processes using Schrodinger's formalism is his "Zur Quantenmechanik der Stossvorgange" (1926c). In his recollections Born implied that his opposition to Schrodinger's realistic wave concepts preceded the actual solution of the collision problem, yet a careful reading of the paper does not disclose any opposition. The paper glows with Born's emotional enthusiasm for Schrodinger's theory. As Born conceded in this paper, he was unsuccessful in his initial attempts to solve the collision problem within the matrix framework but was finally able to obtain the solution with the help of Schrodinger's formalism. This is the reason, Born declared, that he regarded Schrodinger's formalism as "the deepest formulation of the quantum laws" (1926c, 52). The problem of aperiodic collisions required inquiry into the evolution of atomic phenomena. Earlier matrix methods had answered only questions of structure (energy spectra). Moreover, because there is a similarity between the behavior of the atom in collision situations and during its exposure to light irradiation, Born hoped that the solution of the collision problem would pave the way to understanding the interaction between matter and radiation as well. 32 Born's first collision paper clearly asserts the superiority of Schrodinger's theory over Heisenberg's for the solution of this crucial physical problem. Heisenberg's version of quantum mechanics, argued Born, describes only one aspect of quantum problems (stationary states) and says nothing about the occurrence of transitions. In contrast, the onesentence abstract of Born's paper claims that" quantum mechanics in the Schrodinger form allows one to describe not only stationary states but also quantum jumps" (1926c, 52). Born "intentionally avoids" the 32. As Born recalled many years later: "1 wanted to use quantum mechanics because that would give the only way of experimenting with these things. The spectroscopic methods give only terms, energies, nothing more ... the direct way of measuring is by collisions. Even excitation of light in an atom means collision" (interview with Bom, 1963, AHQP).

42

Chapter Two

term "transition probability," using instead Schrodinger's term "amplitudes of vibration." In fact, Born employed Schrodinger and de Broglie's wave concepts quite literally. An atom in stationary state n is a "vibration process" with frequency (1Ih}W~ spread over the whole space. An electron moving in a straight line is, in particular, such a vibration corresponding to a plane wave. When the atom and electron interact, they produce a complex vibration (1.!erwickelte Schwingung; Born 1926c}.33 The wave field determines the atomic transitions probabilistically, and quite independently of the way in which the wave field of the scattered electron is interpreted-literally, or probabilistically in terms of particles.:>! This is the source of Born's noncommittal reference to a putative corpuscular interpretation. As Born conceded later: "It is true that I considered the collision of particles with other particles as a scattering of waves" (appendix to letter to Einstein, 13 January 1929, Born 1971). There is indeed no indication in the paper itself of the staunch belief in particles that Born professed to have. Rather, Born's mind was open on the wave-particle issue. There are several reasons for Born's indecision. It was a common practice at the time to introduce theoretical solutions merely as formal schemes, to be filled with physical content in due time. Schrodinger 33. Heisenberg was unhappy about this literal use of wave concepts: "Ein Satz erinnerte mich lebhaft an ein Kapital aus dem Christ1[ichenJGlaubensbekenntis: 'En Electron ist eine ebene Welle: ... Aber ich will ihnen in Uistem keine Konkurenz machen" (A sentence vividly reminded me of an article of faith from the Christian confession: "An electron is a plane wave." ... But I am not intending to compete with you in slander) (Heisenberg to Pauli, July 1926, PC). 34. To the unperturbed atom with discrete energies Born ascribed eigenfunctions r/tnq.), r/tHqd, ... ; to the unperturbed electron whose direction is detemtined by (a,,8, y) there correspond eigenfunctions of the type sin 21T I A(ax + ,8.'1 + yz + .5). In case the interaction Vex, .'I, z; q.) is taking place, the scattered wave at infinity will be expressed through (Born does not provide the actual calculations in this paper):

r/t~1} (x, .'I, z; q.) = L JJdlAl ••

m

(a, ,8, y) sin k.... (ax + ,8.'1 + yz + .5) r/t'!.. (ql)'

OR

CI'z"IJY+77>U

where T is the energy of the incoming electron, coming from the +z-direction, and IP .... is a function of the energy Vex, .'I, z; q.) of the interaction between the atom and the electron. Concerning the possibility of interpreting this result in terms of particles rather than waves, Born said simply: "U one translates this result into terms of particles, only one interpretation is poSSible: IP .... (a, ,8, y) gives the probability for the electron. arriving from the z-direction, to be thrown into the direction deSignated by the angles el,,8, and y with a phase change I). Here its energy T has increased by one quantum h,,~ at the cost of the energy of the atom" (1926c, 54). The calculated function IP determines the quantum transitions n ~ m, albeit only probabilistically. One does not obtain the actual state of the atom after the collision. only the probability of a certain event (quantum jump).

Matrix Theory in Flux

43

himself introduced his first wave mechanical paper merely as a formal treatment, leaving the question of physical interpretation aside (SchrOdinger 1926a). Similarly, de Broglie left the meaning of his wave concepts vague: "The present theory may be considered a formal scheme whose physical content is not yet fully determined, rather than a fullfledged definite doctrine" (quoted in Jammer 1966,247). It was natural at a time when the foundations of physics were shifting to introduce formal symbolic solutions with minimal interpretive content, especially among mathematical physicists. And Born was indeed" a mathematical method man" (interview with Heisenberg, AHQP). Because there was no elaborate idea of what de Broglie-Schrodinger waves meant, only tentative suggestions, Born preferred to conquer additional territory by mathematical means rather than indulge in a controversy over undefined issues. As Born revealed many years later, his solution to the collision problem did not depend on an interpretation in terms of particles: "I cannot see at all that these purely mathematical objections have anything to do with the question of particles-waves.... For if we accept Schrodinger's standpoint that there are no particles, only wavelets, the scattering calculations would be exactly the same as before" (Born 1953b, 148). Why was Born open at the time to Schrodinger's ideas? Despite the fact that Born recalls James Franck's experiments as a source of his belief in particles, he seemed to consider the wave nature of matter quite seriously, as is clear from a letter to Einstein (Born to Einstein, June 1924, Born 1971). De Broglie's original insights acquired credibility in Gottingen early in 1925 through Einstein's paper "Quantum Theory of the Monoatomic Ideal Gas" (1924). Just as in his previous treatment of blackbody radiation (Einstein 1905), Einstein obtained two terms: one that seemed to correspond to a fluctuation due to particles and another that seemed due to wave interference. In support of de Broglie's concept, Einstein concluded that "it appears that an undulatory field is connected with every motion lBewegul1gsvorgangJ, just as the optical undulatory field is connected with the motion of light quanta. This undulatory field, whose physical nature is for the moment still unclear, must in principle permit its existence to be demonstrated by the correspondingphenomena of its motion fBewegungserscheinungenl" (Einstein 1924, quoted in Stachel1986, 368). We know that these "brief, yet infinitely farseeing" remarks stimulated Schrodinger to look for a wave equation that would describe the undulatory field of matter. Born, after reading Einstein's paper, became convinced that "a wave theory of matter can be of great importance" (Born to Einstein, June 1924, Born 1971), and he supported the efforts

44

Chapter Two

of Walter Elsasser to attribute the Ramsauer effect to the diffraction of electrons.35 It is not surprising, therefore, that when Schrodinger's theory appeared, Born immediately recognized its importance and applied it to the problem of collision phenomena, associating a wave with an electron in the spirit of de Broglie and Einstein. Nor is it superfluous to add here that Jordan, Born's close collaborator, also conceived of Born's initial collision treatment as being a direct continuation of the idea of matter waves in de Broglie's, Schrodinger's, and Elsasser's works (Jordan 1927a). What these matter waves exactly meant was as unclear to Born as to Einstein, Schrodinger, and other participants. Born's elaboration of the corpuscular interpretation, and his later preference for it, as well as Schrodinger's gradual polarization to an overall wave ontology, crystallized through the subsequent dialogue among all the physicists involved. It is not clear whether Born was aware at the time he wrote his first collision paper that Schrodinger and Pauli had each proved the equivalence of matrix and wave mechanics (Schrodinger 1926f; Pauli to Jordan, 12 April 1926, PC). But even if he had been (which is likely), Born could still have considered Schrodinger's version superior. For Schrodinger proved the equivalence between the two theories for bound systems only. Schrodinger also believed that extensions of the theory would be more amenable to his version, proving its superiority. Indeed, he suggested the collision problem as a possible case in point (Schradinger 1926f). Born's statement in his paper clearly echoes Schrodinger's hopes: "Of the different forms of the theory only Schrodinger's has proved suitable for this process [collisions] ... and exactly for this reason I might regard it as the deepest formulation of the quantum laws" (Born 1926c, 52). Born's initial enthusiasm for Schrodinger's ideas is confirmed by the correspondence between the two at the time. Born admitted in a letter to Schrodinger that he was so enraptured by Schrodinger's work that, with "flying banners," he was drawn back again to the clear conceptual structures of classical physics (Born to SchrOdinger, 6 November 1926, AHQP). Born was so impressed that he originally considered Schradinger's theory to have more physical meaning than matrix mechanics (Born to Schrodinger, 16 May 1927, AHQP). This enthusiasm was strongly expressed, according to Born, in his own paper.36 35. The Ramsauer effect is a phenomenon in which the scattering of electrons during collisions with atoms of certain gases deviates strikingly from the classical theory (slowmoving electrons are deflected from their paths much less often than faster moving ones, and the angle of deflection is very small). Elsasser (1925) explained this experimental effect as a diffraction phenomenon of de Broglie waves. 36. Born wrote to SchrOdinger: "You know that immediately after the appearance of your first works I expressed very strongly my enthusiasm for your conceptions in my

Matrix Theory in Flux

45

As was first pointed out by Linda Wessels (1981), Born did not initially connect the wave function with the probability of position; the "'function controlled the energetic transitions of an atom and the energy and direction of motion of colliding electrons. Doubting the possibility of ascribing position to intraatomic electrons, Born questioned the reality of individual electrons within the atom as well: "Matter can always be visualized as consisting of point masses (electrons, protons), but in many cases the particles are not to be identified as individuals, e.g. when these form an atomic system" (1927b, 9). Even though the presence of particles seemed to be implied by the fact that a "disturbance is propagated along a path away from the atom, and with finite velocity, just as if a particle were being thrown out," their existence should not "be taken too literally" (Born 1927b, 10). (Later, of course, Born would change his attitude: " 1'" 12 denotes [the] probability that the electron will be found in the volume-element dv; this holds in spite of the fact that the experiment, if carried out, would destroy the connection with the atom altogether"; Born 1969, 147.) Only in his second collision paper (Born 1926b) do we find the beginning of Born's opposition to Schrodinger. This opposition was not yet militant, though it later became so. Although Born found Schrodinger's idea of wave packets unsatisfactory and proposed his own interpretation of the "'-function as guiding free particles in a "ghostlike spirit" in analogy with Einstein's idea, he nevertheless expressed satisfaction at the retention of the usual concepts of space-time in Schrodinger's theory. Born did not yet foresee the applicability of his conception of the ",-function to the possible motions of particles in the interior of the atom. 37 In his "adiabatic" paper (Born 1927a), Born still did not regard the 3N-dimensionality of Schrodinger's waves for N particles-later to be one of the major arguments against Schrodinger's interpretationas a reason to object to a wave ontology. Only with the development of transformation theory (which reinforced and axiomatized Born's statistical approach) did Born reach his final stand: "Schrodinger's achievements reduces [sic] to something purely mathematical" (Born to Einstein 1926, quoted in Pais 1982, treatise. Heisenberg from the beginning did not share my opinion that your wave mechanics is more physically meaningful than our quantum mechanics; yet the treatment of the simple phenomena of aperiodic processes (collisions) led me initially to believe in the superiority of your point of view. In the meantime, I found myself again in agreement with Heisenberg's position" (Born to SchrOdinger, 6 November 1926, AHQP). 37. "The motion of the particles follows laws of probability, but the probability itself propagates in hannony with the causaIlaw. If three stages of the development of the quantum theory are reviewed, it can be seen that the earliest, that of the periodic processes, is quite unsuitable for testing such an idea.... Nothing fundamental in favor of our statement can be obtained as long as we consider periodic processes" (Born 1926b, 208).

46

Chapter Two

1198).38 Together with Heisenberg and Jordan, and in contrast to his early enthusiasm, Born came to see Schrodinger's wave mechanics as no more than a mathematical appendix to matrix mechanics. To Schr6dinger's total dismay, and despite his desperate pleas for Born to remain open to different interpretive options (Schrodinger to Born, 2 November 1926, AHQP), Born allied himself with SchrOdinger's adamant opponents. Born's opposition to 5chrodinger's ideas became so complete that he indoctrinated younger physicists against them in a "military," albeit "playful" manner.39 Bohr, however, did not agree with the GOttingen attitude, which depreciated entirely the physical meaning of Schrodinger's theory, and proposed his complementarity as a compromise (see chapter 6).

Born's Probabilistic Interpretation and Quantum Jumps According to Born's recollections, every collision experiment conducted by his colleague Franck in the adjacent building at Gottingen was a clear demonstration of the corpuscular nature of electrons, thus prompting Born to suggest an interpretation in direct opposition to Schrodinger's ideas (Born 1961; interview with Born, AHQP). I have already argued that this story does not withstand historical scrutiny. Franck's name is indeed essential in another respect: his famous work (with Gustav Hertz) on atom-electron collisions was generally regarded as direct experimental evidence for Bohr's ideas about stationary states and the discontinuous energetic transitions between them-quantum jumps. In fact, the theoretical quantum mechanical description of these jumps was Born's central aim, as is clear from his first and second collision papers. The abstract of the first collision paper clearly states its main purpose: the theoretical description of quantum jumps with the help of Schrodinger's formalism. Born summarized the essence of his collision papers as a "precise interpretation of just these observations which may be regarded as the most immediate proof of the quantized 38. Born was impressed by Pau Ii's argument that regular pOSition space is not essential, and that by a suitable canonical transformation the description in position space can be converted into a description in momentum space (see Pauli to Heisenberg, 19 October 1926, PC; Born to Schrodinger, 6 November 1926, AHQP). 39. According to Jordan: "Einmal in Gottingen bei einem Spaziergang von Born mit Dirac und Oppenheimer und vielleicht mit noch einem oder zwei anderen ... hat Born also einen Brief von SchrOdinger vorgelesen und Oppenheimer erziihlte mir scherzhaft, Born hatte so wie ein Feldherr seine Truppen zusammenruft, so hatte er den anderen erklart, was fur falsche Ideen das waren die 5chrOdinger da hatte" (Once on a walk in GOttingen with Dirac and Oppenheimer and perhaps with one or two persons ... Born read a letter from Schrodinger aloud, and Oppenheimer told me jokingly that Born, as if he were the commander in chief summoning his army, explained to everybody how false were SchrOdinger's ideas at the time) (interview with Jordan, AHQP).

Matrix Theory in Flux

47

structure of energy, namely the critical potentials that were first observed by Franck and Hertz" (1927b, 11). Born (1927a) further substantiated Bohr's concepts of stationary states and discrete transitions between them by discussing the adiabatic principle in quantum mechanical terms. In opposition to Schrodinger, who wanted to do away with Bohr's "monstrous" concepts by suggesting an alternative, continuous wave ontology, Born fully defended Bohr's ideas. Born's (1927a, 1927b) central inquiry was: to what extent is it possible to harmonize the concept of quantum jumps, so fruitful from an experimental point of view, with Schr6dinger's wave mechanics, so mathematically powerful? As the Bom-Schr6dinger and Jordan-Schr6dinger correspondences reveal, it is around quantum jumps, and not around waves versus particles, that heated controversy evolved. Schr6dinger wrote in a letter to Born that he did not rule out the possibility that Born's ideas were correct. Yet Schr6dinger felt strongly that Born and his colleagues were too addicted to the old concepts of stationary states and quantum jumps. He could not comprehend why an interpretation that does not dogmatically postulate the discontinuities, as the G6ttingen-Copenhagen does, is a priori impossible. His own continuous treatment of resonance between two atoms (Schr6dinger 1927b) led to the same consequences as the theory that postulated discontinuous exchanges of energy (Heisenberg 1927a). Does not this indicate, inquired Schr6dinger, that one should explore whether all other discontinuities can be similarly deduced rather than dogmatically postulated (Schrodinger to Born, 2 November 1926, AHQP)? In his reply to Schr6dinger, Born conceded that after the appearance of Schr6dinger's theory, he was at first disposed to return to the clear conceptual framework of classical physics. But he changed his mind. Of course, Born agreed with Schrodinger, it is desirable to explore all possibilities, yet he himself did not intend to do so. Instead, Born had decided to rely on his own feeling that one cannot dispense with quantum jumps (Born to Schr6dinger, 6 November 1926, AHPQ). In his second collision paper (Born 1926b), Born spelled out the connection between a system's stationary states and Schr6dinger's wave function. For a periodic system (an unperturbed atom, say) represented by I/I(x) = LC.l/ln(q) (discrete spectra), Born proposed that 1C.12 is the "frequency" of the state n in a group of identical noncoupled atoms. In other words, 1en 12 denotes the probability that the system is in a stationary state described by I/,,,(q). Born's interpretation of 1C ,,12 as giving the probability of the stationary states of the system was a pregnant idea. It shifted the probability considerations one level deeper, from transitions to stationary states,

48

Chapter Two

thus making the transition probabilities calculable from the more elementary probabilities of these states. This point would be crucial in the Copenhagen deliberations on indeterminism (see chapter 3). Born and his contemporaries initially viewed the probabilistic interpretation of stationary states as the crux of his interpretive achievement. 40 Precisely because this hypothesis for atomic states and transitions was farther reaching and more speculative than Born's relatively straightforward, even obvious, suggestion for free particles, he and his contemporaries saw his interpretation of 1C" 12 as a possibly fruitful conjecture, still in need of experimental verification, rather than an "obviously" correct interpretation. 41 It was Pauli who generalized Born's suggestion concerning the probability of stationary states and endowed this concept with particlekinematic meaning. Born deemed it meaningful only to talk about energies and angular momenta of stationary states. Pauli, however, defined 1I/!(qlt ... , q,) 12 dql' . ·dq, as the probability that, for a definite stationary state, the coordinates qk of the particles (k = 1, ... , f) lie between qk and qk + dqk (pauli to Heisenberg, 19 October 1926, PC). This was actually the first time the wave function had been described as giving the probability of the positions of intraatomic particles. Pauli's definition later appeared in print, in a footnote to a paper on gas degeneracy and paramagnetism (Pauli 1927, 83). 40. Jordan, discussing recent developments in physics, characterized Born's contribution as allowing the determination of the probability that an atom is in a definite stationary state at a definite moment in time: In Verfolgung seiner Vorstellungen hat Born die physikalische Bedeutung der Schrodingersc1ren We1lenfuktion schiirfer bestimmen kOnnen. Er hat gezeigt, dass man mit ihrer Hilfr ein Maass tier Wahrsdleill/iCh/cL'it dtlfiir angeben Ieann, dass ein Atom zu einem gewissen Zeitpunkt sich gerade im n-ten Quantenzustande befindet. Diese Deutung der Schrodingerfunktion konnte :~estiitzt werden durch den Nachweis, dtlss das beleannte Ehrenfostsche Adiabatenprinzip der Quantenthrorie im Anschluss all diese Deutung auch rom Standpunkte der neuen Quantenmechanik formuliert und bewiesen werden konnte. (1927a, 646) (In further developing his conceptions, Born succeeded in defining more precisely the physical meaning of SchrOdinger's wave function. He demonstrated that with its [wave function's] aid, one could determine the value of the probability for an atom to be in the nth quantum [stationary) state at a certain moment in time. This interpretation of Schrodinger's wave function was corroborated by demonstrating that Ehrenfest's familiar Adiabatic Principle of quantum theory could also be formulated and proved from the standpoint of the new quantum mechanics in conformity with this [Born's) interpretation. ) 41. Born emphasized this point at the time: "It is, of course, still an open question whether these conceptions can in all cases be preserved .... Unfortunately, the present state of quantum mechanics only allows a qualitative description of these phenomena [collisions of electrons with atoms-in particular, collisions of electrons in helium)" (1927b,11-12).

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Pauli, who had stood somewhat aloof from the development of matrix mechanics, was not as hostile to Schr6dinger as Heisenberg was, nor did Pauli subscribe to the opinion that the positions of intraatomic electrons are unobservable in principle.42 Thus Pauli favored resuscitating the visualization of the stationary states through the kinematic data of positions of intraatomic particles. Pauli's contribution, which stimulated Heisenberg's own revival of regular space-time through the uncertainty principle (see chapter 4), was indeed a landmark on the way to the establishment of a particle ontology of quantum physiCS. No such particle ontology had underlain Born's original interpretation. Born's own calculations for the collisions between electrons and hydrogen atom were carried out only to a first approximation. Therefore, Born concluded, "it would be decisive for the theory if it should prove possible to carry the approximation further" (1927b, 13). In his textbook Atomic Physics, written in 1935, Born emphaSized the importance of verifying his original hypothesis by subjecting scattering and other phenomena to precise quantum mechanical calculations (Born 1969). Born mentioned in this respect his and Vladimir Fock's work on the excitation of atomic systems, Dirac's work on the excitation of coupled systems, Born's and Mott and Massey's work on collisions, and Wentzel's verification of the Rutherford formula. Such experimental confirmation was, according to Born. more important than philosophical elucidation. This process of critically evaluating and modifying Born's Original ideas is still going on. Eugen Merzbacher (1983) has described advances in ion-atom collisions as, in many cases, substantiating Born's work. Abraham Pais (1982) has described his own success in carrying out a calculation for scattering by a static, spherically symmetrical potential, and his failure to extend Born's method to relativistic field theories. "To this day, proof or disproof of the convergence of the Born expansion in field theory remains an important challenge yet to be met" (Pais 1982, 1198). Recent work on scattering deals with both mathematical improvements and experimental physical difficulties (Daumer 1996; Cushing 1990). The meaning and the foundational status of the Born-Pauli probabilistic interpretation remain today a subject of lively controversy (Diirr et al. 1992a, 1992b, 1996; Valentini 1996). What appears in textbooks and philosophical writings to be a closed box has never been sealed off at the frontier of research. 42. According to Leon Rosenfeld (1971). Pauli did not welcome a complete break between the fonnalized conceptual scheme of matrix mechanics and the classical notions of space-time and Keplerian orbits that underlay it.

CHAPTER

3

~

Quantum Philosophy in Flux The external conditions, which are set . .. by the facts of experience, do not permit him [the scientist1 to let himself be too much restricted in the construction of his conceptual world by tlte adherence to an epistemological system. He therefore must appear to the systematic epistemologist as a type of unscrupulous opportunist. Albert Einstein 1949b, 684

Introduction In the previous chapter I argued against the widely accepted miscon-

ception that the GOttingen-Copenhagen physicists developed matrix mechanics by implementing a committed indeterministic corpuscular ontology as opposed to Schrodinger's causal wave ontology. I also argued that the two approaches were not conceptually distinct and historically independent. I described the development of the GottingenCopenhagen version of quantum mechanics as characterized by vacillation on foundational questions and openness to the wave theoretical perspective. Perhaps the strongest expression of this openness, if not preference, is a statement Max Born made during his lectures in the United States in 1926: Heisenberg's matrix elements are not amplitudes of radiation but "real waves of an atom" (1926a, 70). The polarization and conflict between the wave theoretical and matrix approaches was indeed the result of the threat Schrodinger posed to matrix theorists; acknowledgments of mutual debt were largely eliminated from the public discourse. Yet the development of the GOttingen-Copenhagen version depended, in part, on the de Broglie-Schrodinger ideas-as a stimulus to response and as a resource for selective appropriation. De Broglie'S work reinforced Bohr's realization that one had to dispense with particle space-time models in the quantum domain (Bohr 1925); this realization was implemented in Heisenberg's reinterpretation paper (1925). Wave theoretical imagery informed Jordan's early treatment of electrodynamics in matrix mechanics and guided his pioneering work on the theory of quantized matter waves (Darrigol 1986; Kojevnikov 1987).

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Chapter Three

Another widely held misconception is that a positivist philosophy of "elimination of unobservables" was central to the emergence of the theoretical structure of the new quantum theory. It was this positivist philosophy, so the story goes, that guided Heisenberg's efforts from his reinterpretation paper to his uncertainty paper (Hendry 1984). I argue that positivist philosophy was less a heuristic principle and more a tool with which theoretical advances could be justified ex post facto. Contrary to the received opinion that Heisenberg's philosophical stand remained stable from the reinterpretation (1925) to the uncertainty paper (1927b), a careful analysis reveals a radical change, if not an about-face. Heisenberg employed two different strategies of justification: the Machean positivist principle of elimination of unobservables in his reinterpretation paper and the operational approach of defining physical concepts through the procedure of their measurement in his uncertainty paper. If in 1925 Heisenberg claimed that directly observable experimental data (frequencies and intensities of emitted radiation) should determine theoretical structure, in 1927 he declared that it is theory that gives meaning to experiment: "It is the theory which decides what we can observe" (1971, 77). No coherent philosophical choice between positivism and realism guided Heisenberg's efforts. A fascinating, ever changing mixture of realist intuition and positivist legitimation characterizes Heisenberg's work leading to, and springing from, the reinterpretation paper. Positivism in Flux The myth of the fundamental heuristic role of the elimination of unobservables originated with the matrix physicists themselves. Born declared in his presentation of the new theory in winter 1925-26 (as well as in later writings) that Heisenberg ended the crisis in physics by introducing a fundamental epistemological principle that could be traced back to Ernst Mach. This positivist principle states that concepts and representations that do not directly correspond to observable "facts" are not to be used in a theoretical description of reality (Born 1926a, 68-69).1 Heisenberg, supposedly, was encouraged by Einstein's example-in 1905 Einstein ended another major crisis in physics using the principle of elimination of unobservables. Heisenberg banished the picture of electron orbits and the concept of "electron position within 1. Instead of such unobservable kinematic variables as the position. velocity, or period of revolution of an electron in an atom, Heisenberg incorporated experimentally observable spectroscopic data (frequencies and intensities of radiation) into the theoretical framework.

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the atom," Born claimed, for the same epistemological reasons that Einstein had eliminated the concepts of absolute velocity and absolute simultaneity. Historical research leads to a different picture (MacKinnon 1977; Mehra and Rechenberg 1982; Beller 1983, 1988; Hendry 1984). During the years preceding Heisenberg's reinterpretation paper, quantum physicists increasingly encountered the inadequacy of the notion of intraatomic orbit. When physicists questioned the adequacy of orbital notions, their doubts had more to do with the theoretical failure of orbits than with their experimental unobservability. Orbital assumptions failed in the domain of the interaction of light with matter; they could not be reconciled with the fact that the dispersion of light occurs with spectroscopic rather than orbital mechanical frequencies. Moreover, in the domain of the constitution of atoms and molecules (with the full price of ad hoc assumptions), all modifications of the orbital mechanical models failed to do justice to the experimental state of affairs (Hendry 1984). Nor did it help much to attach to these models a formal symbolic, rather than realistic, significance. The orbital model failed for the anomalous Zeeman effect, and for the spectrum of the helium atom. As Born attempted to argue in 1924, all possible orbital assumptions led to equally wrong results (Hendry 1984).2 Gradually it became clear that there was really no good reason to cling to the failed orbital concepts and the mechanical models built on them. The need now arose, as Pauli understood, for a new, more adequate kinematic law of motion and perhaps too for a new dynamic law responsible for the changes in kinematics. It seemed reasonable at this point to introduce the so-called virtual oscillator model, first applied to the interaction of light and matter, and soon extended to theories of atomic structure. In the domain of the interaction of matter with radiation, this symbolic model proved to be a powerful tool for translating and extending successful classical formulas into the quantum domain via the correspondence principle (DarrigoI1992a). Reaching the conclusion that "reality was not in orbits, but rather in Fourier components, or rather their quantum mechanical analogues" (interview with Heisenberg, AHQP), and encouraged by his previous results (Kramers and Heisenberg 1925), Heisenberg decided in the middle of May 1925 to attack the problem of hydrogen line intensities. Heisenberg's correspondence with Ralph Kronig, whom he kept informed about his progress, clearly reveals that epistemological considerations were far from Heisenberg's mind during his first attempts 2. Today we know that at the price of nonlocality one can retain space-time trajectories

within an atom (for example, Bohm's theory).

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Chapter Three

to tackle the problem.3 The hydrogen problem was too complicated mathematically, and Heisenberg had to content himself with the simple case of a harmonic oscillator. Even in this case, mathematical difficulties remained, and Heisenberg was not yet sure what physical consequences his new scheme implied: "The physical interpretation of the above mentioned scheme yields very strange points of view" (Heisenberg to Kronig, 5 June 1925, AHQP). Heisenberg confessed to Pauli that his private philosophy was simply" a mixture of all possible moral and aesthetic calculations and rules" through which he did not "find his way anymore" (Heisenberg to Pauli, 24 November 1925, PC). In a letter to Pauli, Heisenberg argued that the interpretation of the experimental formula for the hydrogen spectrum on the basis of kinematic orbital concepts was impossible: " An interpretation of the Rydberg formula in terms of circular and elliptical orbits does not have the slightest physical significance." He added that his efforts were devoted to "killing the concept of an orbit which cannot be observed anyway" (Heisenberg to Pauli, 9 June 1925, PC). The order of precedence seems clear: orbits are theoretically inadequate, and they had therefore better be eliminated. One can dispense with orbits without regret because they do not have any observational significance. A comment on the possible influence of Pauli on Heisenberg is in place here. Most historians who treat this subject (Hendry 1984; Serwer 1977) assume that Pauli's operational attitude called for the elimination of the orbits and positions of intraatomic electrons because they are, as Hendry puts it, "operationally meaningless." Heisenberg's reinterpretation paper is often perceived as an implementation of Pauli's epistemological program. Yet this point of view needs to be qualified. It is true that, at least after 1919, Pauli advocated in certain theoretical contexts an operational attitude toward physics. For example, he claimed that the strength of electric fields in the interior of an electron is a meaningless concept because the field strength is defined as a force acting on a test body, and there are no smaller test bodies than the electron itself. Similarly, the concept of continuous space-time in the interior of the electron is meaningless. Pauli argued that" one should 3. In a letter to Kronig, Heisenberg's program is clearly stated: In classical theory, Heisenberg wrote, knowledge of the Fourier series is sufficient to calculate the radiation completely, not only dipole moments but higher moments as well. In principle, one should be able, by replacing classical variables with their quantum analogues in the equation of motion, to obtain an exact, complete expression for the intensities. Because Heisenberg wanted to take into consideration quadruple and higher moments, he had to immerse himself in the technical mathematical problem of what multiplying X and Y meant, when X and Y were algebraic sets of quantum substitutes for classical poSition coordinates (Heisenberg to Kronig, 5 June 1925, AHQP).

Quantum Philosophy in Flux

55

adhere to introducing only those quantities in physics which are observable in principle" (quoted in Hendry 1984, 19). However, the key phrase here is "in principle." The question was not whether the force acting on the electron could be experimentally measured but whether the definition of the concept of field strength was consistent with the hypothetical possibility of measurement. Because the electron was assumed to be the smallest test body, it was meaningless (according to the operational approach) to talk about space-time in the electron's interior, but it was not meaningless to talk about the position of this smallest test body in the larger atom. There was nothing inconsistent in assuming that in principle electron position could be measured in the interior of an atom, though the state of experimental techniques did not allow it in practice. One could, for example, devise a y-ray thought experiment-such as Heisenberg proposed later in his uncertainty paper. And if electron positions are not unobservable in principle, the same holds for electron orbits. Pauli's stand, pushed to its logical conclusion, implied merely that intraatomic positions and trajectories could be determined only with the accuracy of the size of the electron-the smallest particle known at the time. And, in fact, Pauli did emphasize in a letter to Eddington of 20 September 1923 (PC) that the electron's position need not be considered unobservable in principle, and that the question of technical difficulties should not enter into considerations of principle connected with the definition of physical concepts.4 As already mentioned, Heisenberg was led to his reinterpretation procedure by trying to solve the problem of hydrogen intensities. His attempt did not succeed. Heisenberg was forced, by technical difficulties, to stop at the programmatic point. Had he solved this problem, Heisenberg's motto "success sanctifies the means" would suffice to justify the procedure of replacing the classical coordinates with a set of quantum theoretical magnitudes. Yet at this programmatic point, Heisenberg needed a more general conceptual justification, and he chose the principle of elimination of unobservables. 5 This principle, sup4. Not by accident did Pauli fail to mention the principle of elimination of unobservabies when presenting the essentials of Heisenberg's approach in his paper on the hydrogen atom (pauli 1926b). Significantly, it was Pauli himself who later restored the kinematic positions of intraatomic electrons in his extension of Born's probabilistic interpretation. 5. Why did Heisenberg not use Bohr's correspondence principle instead, a principle that had played a most fundamental role in his reinterpretation procedure? The most probable reason is the collapse of the Bohr-Kramers-Slater theory (1924) and its associated research program. In this theory, the correspondence principle, the wave nature of radiation, and nonconservation were tightly connected-and the refutation of the BohrKramers-Slater theory by the Bothe-Geiger experiments seemed to indicate that the cor-

56

Chapter Three

ported by Einstein's authority, was a clever strategic choice. Precisely because it was only invoked a posteriori it played no essential role in the derivation of the formulas in the reinterpretation paper (1925). The reinterpreted formulas held true whether one held the position of electrons to be observable or not. The matrix formalism was not undermined after Heisenberg changed his opinion about the observability of electrons in his uncertainty paper (1927b). The above analysis demonstrates that the elimination of unobservables was, in fact, not a guiding principle, but rather a general justification of a powerful technical method that de facto eliminated classical positions and orbits. The elimination of the space-time container and the loss of visualization were prices to be paid, not goals to be attained. Not surprisingly, the authors of matrix mechanics sometimes would talk not in terms of" observable in principle" but rather in terms of what "can be observed experimentally" or what is "really observable" (Born 1926a, 69).6 One of the weapons Gottingen-Copenhagen physicists wielded against Schrodinger's competitive approach was an accusation of anachronistic, "naive" realism. Yet Heisenberg and Schrodinger, despite a difference in intellectual style, were not far apart on the issue of realism. Both employed visualizable intuitions; both willingly sought new "artifices of thought" when old ones failed; both engaged in heated controversies about the "reality" of certain scientific notions (quantum discontinuities, !/I-functions). In fact, heated controversies about unobservable "reality" played a decisive part in the genesis of interpretations of quantum physics. Thus the reality of quantum jumps was the central issue in the interpretive efforts undertaken during the crucial years 1925-27. Indeed, this issue channeled the efforts of the "positivist" group made up of Born, Heisenberg, and Jordan no less than it did those of the "realistically" inclined Schrodinger (see chapters 4 and 6). When, in his reinterpretation paper, Heisenberg replaced the familiar classical parameters of motion with abstract algebraic constructs, the basic physical intuition behind his innovation was that there must be a correspondence between the internal dynamical "mechanism" of an respondence principle could no longer lead to progress. Indeed, Einstein objected in a letter to Heisenberg that his approach in the reinterpretation paper was too close to the discredited Bohr-Kramers-Slater theory. Serious doubts about the fundamental role of the correspondence principle had been expressed even before the Bothe-Geiger experiments. Sommerfeld, Heisenberg's teacher, declared in 1924 that the correspondence principle was not part of the foundation of quantum theory-it was merely its limiting theorem (Mehra and Rechenberg 1982). Pauli similarly denied the ability of the correspondence principle to be a faithful guide for understanding the structure of atoms (Mehra and Rechenberg 1982). 6. A more detailed analysis of the role of operationalism in the erection of quantum theory is given in Beller (1988).

Quantum Philosophy in Flux

57

atom and the radiation it emits. Heisenberg's "realistic" presupposition "that something in the atom must vibrate with the right frequency" (Heisenberg to van der Waerden, 8 October 1963, van der Waerden 1967) prompted him to construct a bizarre noncontinuous space (through a reinterpretation of kinematics) so that electron "motions" in this space would have the correct spectral frequencies. The advantage of gaining a physical sense of the underlying atomic model came at the price of abandoning visualization in regular space-time and was justified by the positivist ideology of elimination of unobservables. 7 Schrodinger shared Heisenberg's conviction that a connection must exist between electron motion and radiation frequencies, yet he did not have Heisenberg's inclination to operate in nonclassical spaces tom, as Schrodinger called it, by "yawns" and "gaps." Schrodinger announced that "what we cannot comprehend within it [regular space-time] we cannot understand at all" (1926b, 27). He offered his own wave mechanism, which preserved the direct relationship between electron motions and radiation frequencies. The contrast between Heisenberg and Schrodinger is not adequately described as a realist-positivist dichotomy. The difference between them lies elsewhere. Shifting theoretical and social circumstances forced Heisenberg to abandon the positivist position that he advocated in his reinterpretation paper. In his uncertainty paper, Heisenberg emphasized not the close proximity of basic theoretical terms to direct sense perceptions (what can be closer to Machean sense perceptions than the frequency and intensity of light, or, in other words, light's color and brightness?) but the supremacy of theory over facts (a good theory is not refutable by facts; a good theory is needed to define what the facts are). Heisenberg's interpretive attempts can hardly be viewed as a smooth evolutionary process, guided by consistent epistemological concerns. What we have witnessed, rather, are changes of opinion on basic issues, trial and error, about-faces. But though extraordinarily agile, Heisenberg was not the only physicist who skillfully adapted himself to changing theoretical opportunities. Pauli, for example, expressed the opinion in 1925 that probability statements should not enter into the basic postulates of a satisfactory physical theory, only to become one of the architects of the probabilistic kinematic interpretation of the wave 7. Heisenberg's physical intuition was obscured by Born and Jordan's chillingly elegant matrix formalism; Heisenberg's original awkward mathematical formulation contained phYSical heuristics that did not appear in the matrix formulation. This is exactly what Pauli feared when he refused to collaborate with Bom, telling him that his "tedious and complicated formalism ... is only going to spoil Heisenberg's physical ideas" (quoted in van der Waerden 1%7.37).

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Chapter Three

function two years later. Nor do we find consistency between the epistemological views of quantum physicists and their actual scientific practice. Pauli, who asserted the need to replace orbits in atoms with more satisfactory kinematics two years before Heisenberg's reinterpretation, continued research based on orbital assumptions. Einstein. at least in his younger years, refused to be restrained by an epistemological straitjacket. In his discussion with Pauli in the 1920s, when Pauli argued that the continuum must be abandoned on operational grounds, Einstein replied that the issue must be decided only on the basis of what was theoretically functional (Hendry 1984). Nor did Niels Bohr consider philosophical analysis heuristically valuable. He did not take seriously considerations of simplicity, elegance, or even consistency (the "epistemic virtues"), holding that "such qualities can only be properly judged after the event" (Rosenfeld 1967, 117). A harsh and crisp verdict came from Paul Dirac: "I feel that philosophy will never lead to important discoveries. It is just a way of talking about discoveries which have already been made" (interview with Dirac, AHQP). While the above quotes seem to indicate that philosophy is always used only a posteriori, in the "context of justification," as opposed to the "context of discovery," such an assertion would be too categorical. Quite apart from the fact that a meaningful distinction between the context of discovery and the context of justification cannot always be sustained, the sources of scientific creativity can be found in diverse fields of human activity-philosophy is not the most unlikely of them. Philosophical ideas might be suggestive in particular theoretical settings: the idealist German philosopher Fichte might have been a surprising source of Heisenberg's idea of the reduction of a wave packet (see chapter 4). Historians of science have described extensively the rich cultural and political milieu in which the development of quantum mechanics took place (Faye 1991; Forman 1971, 1979; Heilbron 1987; Holton 1970; Krips 1996; Wise 1987). Yet these contexts served more as resources and less as influences. The point is not that philosophy cannot influence science. Creative scientists might adopt a certain foundational stand (sometimes indistinguishable from a traditional philosophical stand) in order to pursue a definite line of research. Such a philosophical orientation is, however, local and provisional. The longevity of philosophical "commitment" is coterminous with its usefulness in solving the problem at hand. s 8. A scientist can develop a preferred philosophical position, yet such a position crystallizes only after an entire career, when certain basic characteristics of successful theories that the scientist has developed are internalized and "entheorized." For the notion of "entheorizing," see Fine (1986) and chapter 9.

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Indeterminism in Flux I argued in chapter 2 that one should not ascribe to Born any committed opinions about particle ontology or about the physical significance of Schr6dinger's theory; these were issues that Born initially left open. My claim applies similarly to the problem of indeterminism. Heisenberg, I have argued (chapter 2), was open on the question of determinism versus indeterminism. I will argue, as well, that Born did not have a committed opinion about causality, only tentative, uncommitted suggestions. 9 My analysis of Born's stand will focus on two issues: the nature of positivist statements in quantum mechanics and the problem of elementary probabilities. Born's indeterminism in his first collision paper was rather hesitant: "I myself am inclined to give up determinism in the world of atoms. But that is a philosophical question for which phYSical arguments alone are not decisive" (1926c, 54). He wavered even more in his second collision paper (1926b): even though Born himself inclines toward indeterminism, he fully realizes that attempts to look for "hidden" internal parameters, which determine individual processes, are consistent with the prevailing state of quantum theory. And even later, when Born did commit himself publicly to indeterminism, he confessed in a letter to Einstein that the issue is undecidable in principle (Born to Einstein, 13 January 1928, Born 1971). Born's main concern at the time was neither deep conceptual analysis nor philosophical deliberation, but the solution of the collision problem. As Born indicated in an interview with Kuhn, he did not think his solution involved any far-reaching implications for the issue of indeterminism: "I did not consider it very philosophical. I thought giving up the description in space and time and replacing it by symbolic description was much deeper and much more philosophical. And to find a way of expressing it in simple terms-probability-seemed to me not so very important. ... We were so accustomed to making statistical considerations, and to shift it one layer deeper, seemed to us not so very important" (interview with Born, AHQP). The description of collision phenomena that Born provided was statistical: one does not get an answer to the question "What is the state after collision?" but rather to "How probable is a specified outcome of the collision?" (1926c, 54). Because the necessity of indeterminism was 9. For a different opinion, see Forman (1979). I use the words "causality" and "determinism" interchangeably here, following the usage of quantum physicists. In a careful philosophical discussion these notions need to be dissociated. For a wide-ranging analysis of the complexity of the notion of determinism, and of the application of this notion in different branches of modem physics, see Earman (1986).

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far from obvious, Born had to face a natural question: was his solution only tentative and a more complete, detenninistic description possible in the future, or was his contribution fundamental and not susceptible to any substantial modification? In short, Born was looking for arguments to legitimate his contribution, as is often done in theoretical physics. lO Moreover, Born had a special need for such justification because, in his treatment, the statistical conclusions followed from exact data: even though the momentum and energy of the incoming electron, as well as the energy of the stationary state of the atom, were given, his description of the result of the collision was probabilistic. This situation was clearly unsettling after the Bothe-Geiger experiments, which seemed to indicate that individual atomic phenomena are determinate (that conservation laws apply strictly; Bothe and Geiger 1925a, 1925b). Born tackled this problem from two different angles. He denied an analogy between his solution and the Bohr-Kramers-Slater theorydiscredited by the Bothe-Geiger experiments- despite a very close resemblance between them (Born 1927b, 10 n; Born to Schrodinger, 6 November 1926, AHQP).ll The conservation laws in collisions are enforced, Born claimed, by the basic formalism of quantum theory (1927b, 10 n). He tried to justify his statistical solution by positivist arguments: because formal quantum mechanics renounced "internal atomic motions," there is "no reason to believe that there are some inner properties of the atom which condition a definite outcome for the collision" (1926c, 54). Yet Born must have realized at the time that the renunciation of space-time as a container of motion was far from necessary. As I have mentioned, Heisenberg's claims that electron position within an atom is in principle unobservable were faulty: intraatomic position is unobservable not in principle but merely in practice. And because positivist arguments for the nonexistence of internal atomic parameters, or "hidden variables," were inconclusive, similarly inconclusive were assertions about indeterminism based on such arguments. This is the reason 10. Discussing quantum mechanical and semiclassical solutions in collision processes, Merzbacher (1983) remarked: "The virtues or disadvantages of a partially, or even fully, classical approach are frequently contrasted with the quantum mechanical approach. but since convenience often dictates the choice, such comparisons are usually biased by the desire to justify a particular calculation after its completion." 11. The analogy between the Bohr-Kramers-Slater theory and Born's collision theory is in fact very close. The electronic "phantom" (Po. qo)I'dq the probability that q lies in (qn. qll + dq) when another mechanical variable has the value p. Similarly. the probability that Q takes a value in (Qo. Qo + dQ) while q has the value qo is given by !t/I(qo. Qo}!'dq. Then the probability that Q lies in the interval (Qo. Qo + dQ) whilep = Po is given not. as in the classical case. bydQ-J4> I(Po,q)I'·!t/I(q.Qo)!'dq but rather bydQ·!(Pn. Qn}!'. where (po, Qo) = f4>(Po.q}t/l(q. Qn}dq(Jordan 1927a.647).

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treatment in terms of particles. Yet the appeal of wave imagery is too powerful and its utility for "pedagogical" purposes is too appealing, so even Heisenberg and Paull often preferred to use the matter wave presentation of individual particles. (See the discussion later in this chapter.) As opposed to the partial analogy between waves and particles contained in the idea of a wave packet, the Born-Paull-Jordan idea of the interference of probabilities allowed an overarching analogy between matter and radiation. The fact that the interference of probabilities in Schrodinger's formulation corresponds exactly to the rules of multiplication for matrices with infinitely many rows and columns confirmed the great generality of this new probabilistic framework of quantum mechanics (Jordan 1927a, 647). All existing versions of quantum mechanics-Heisenberg's matrix mechanics, Schrodinger's wave mechanics, Born-Wiener's operator calculus, and Dirac's c-number calculus-were united in the single, powerful formulation of probabilistic transformation theory. That the theory was probabilistic did not seem too high a price compared with its assets of unity, generality, and problem-solving power. The unity and generality of a comprehensive probabilistic quantum theory was the most powerful argument for the indeterministic character of the quantum world and for the duality expressed in the interference of probabilities. For Heisenberg, all his previous intuitive discussions with Bohr about the duality of waves and particles were at once superseded by the unity and beauty of the newborn mathematics. Schrodinger thought otherwise. Since 1925, when he became familiar with de Broglie's and Satyendra Nath Bose's ideas, he had realized that Bose-Einstein counting undermines the idea of an individual distinguishable particle. Particles in a gas had to be replaced by "energy excitation states" (Schrodinger 1926g), and the corpuscular picture of a gas had to be replaced by de Broglie waves. This insight spurred SchrOdinger's theoretical efforts, culminating in the crowning achievement of the creation of wave mechanics (Wessels 1979). For the rest of his life Schrodinger, considering the concept of an individual particle bankrupt, advocated an underlying wave ontology, rather than the synthesis, or "coexistence," of waves and particles in the spirit of de Broglie and Einstein (Bitbol 1996; Beller 1997a). Understandably, Schrodinger did not embrace the corpuscular statistical ontology offered by Heisenberg and Born. Heisenberg also realized very early that the Bose-Einstein statistics undermines the idea of an individual particle and used this conclusion initially to argue against the possibility of intuitiveness, or Ansc1Ululichkeit, in the rnicrodomain (Heisenberg 1926b). He later minimized the implications of the Bose-Einstein statistics in his interpretive writings when confronted with Schrodinger's competing, wave theoretical endeavors.

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In 1925-27, that period of "human confusion," support for Schrodinger's position came from unexpected quarters. Though he attacked Schrodinger publicly for deviating from, and challenging, Bohrian guidelines (especially on the issue of quantum jumps), Jordan's theoretical efforts were much closer in spirit to Schrodinger's than to Bohr's ideas.lO As noted by several authors, matrix theorists were familiar with, and even actively participated in, an elaboration of the wave theoretical point of view (Beller 1983; DarrigoI1986; Kojevnikov 1987; see also chapter 2). Jordan, a founder of second quantization, is the most prominent case. Following de Broglie and Einstein, Jordan made many important advances using the assumption of a complete analogy between matter and radiation as a heuristic principle. In Jordan's hands, the fruits of the matter wave analogy included a theoretical proof of electron diffraction-before the experiments by Davisson and Germer that demonstrated the diffraction of an electron beam-as well as Jordan's early conjecture that matter could be created and destroyed (Darrigol1986, 219). As early as the Bom-Heisenberg-Jordan paper, Jordan had obtained light quanta by quantizing the Maxwell fields (this part of the paper was written by Jordan alone). As soon as Jordan learned about Schrodinger waves, he contemplated the possibility that matter as well could be represented by quantized "'-functions. His presumption of an analogy between matter and radiation led naturally to the idea that classical individual particles might be replaced by wave excitations in the case of matter as well. Jordan had very little encouragement from Heisenberg; Born, initially sympathetic to the idea, soon withdrew his support (DarrigoI1986,219).11 Jordan's quantized matter waves in three-dimensional space reinforced Schrodinger's wave theoretical position, by removing the multidimensionality of the "'-function as an argument against Schrodinger's wave ontology. There was a meaningful similarity between Jordan's matter waves and the quantized waves Schrodinger used to explain Bose's statistics before his discovery of wave mechanics. If for Heisenberg second quantization implied the equivalence, or mutual translatability, of the wave and particle models, for Jordan the wave theoretical substratum was the more basic of the two. Like Schrodinger, Jordan was willing to give up the primacy of atomistic ideas. In this theoretical context Jordan held that the discontinuity of both matter and light can be derived from wave quantization: liThe existence of atoms is no longer a primary basic fact of nature; it is only a special part of a 10. Jordan's theoretical work, and his crucial role in the history of quantized matter waves, is analyzed extensively in Darrigol (1986). 11. Born may have withdrawn his support because of his change of heart regarding the physical significance of Schrodinger's wave ontology (chapter 2).

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much more general and comprehensive phenomenon-the phenomenon of quantum discontinuities (1944, 144-46, quoted in Darrigol 1986). Schrodinger, as we know, did not perceive second quantization as implying equivalence between wave and particle pictures in the spirit of Heisenberg, for by this procedure one "cannot avoid leaving indeterminate the number of particles dealt with. It is thus obvious that they are not individuals" (1950, 112). The fascinating history of wave-particle concepts cannot be fully understood without introducing the history of quantum electrodynamics (QED), which is beyond the scope of this book. Let me simply mention two important points. First, different scientists deduced different philosophical conclusions from the same, or very similar, mathematical procedures. While not discussing these issues explicitly, their experience and knowledge of QED informed their popular writings, which were confined, as it were, to the nonrelativistic theory of quantum mechanics. This state of affairs produced contradictions, most prominently in Heisenberg's case. The second point is that even for the same author, the relative primacy given to particle versus wave concepts changed from one theoretical context to another. Thus, in their early comprehensive program for QED, Pauli and Heisenberg (1929) assumed the "symmetry," or equivalence, of wave and particle schemes. Later, disappointed by the difficulties they encountered, Pauli preferred to emphasize the dissimilarity between matter waves and light waves (matter waves are not directly observable-r{! is a symbolic quantity). Similarly, Dirac, whose efforts were initially guided by a preference for particle concepts, in his later years gave much more support to the symmetrical interpretation of second quantization (Darrigol1986). Important advances using second quantization were possible without a resolution of the wave-particle dilemma: Fermi and Fock, for example, used formal theoretical arguments in their work (a chargesymmetry argument, an argument of nonconservation of particle number). In conclusion, no paradigmatic consensus was achieved, and indeed none was needed, to ensure outstanding theoretical progress (DarrigoI1986; Schweber 1994). No unchanging philosophical meaning can be attached to such creative theoretical efforts, even if these efforts can be reconstructed as being directed toward the same foundational issue-the wave-particle dilemma. Ambiguity and the Wave-Particle Issue

The proliferation of opinions, or perspectives, on the wave-particle issue was connected with the ambiguity of the designating terms. There was no agreement on the necessary and sufficient attributes of a particle. Einstein and Schrodinger argued that it is unreasonable to give up

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the joint applicability of position and velocity variables as belonging to the very definition of a particle. For Schrodinger, the indistinguishability of particles, implied by the new quantum statistics, signified the total bankruptcy of the concept of a particle, and the continuing use of particle concepts offended his theoretical sensibilities. What Schrodinger found so objectionable in the idea of a particle was that "it constantly drives our mind to ask for information which has obviously no Significance.... An adequate picture must not trouble us with this disquieting urge; it must be incapable of picturing more than there is." According to Schrodinger, the problem with the concept of a particle was that it "exhibits features which are alien to the real practice" (1950, 111). In the microdomain, the only "tolerable image" of even an isolated particle is "the guiding wave group" (1950, 115). For Bohr, this was an indication of the limitation of classical concepts, not an indication that they should be given up. Feynman's verdict was crisper: "It [the electron] is like neither" (Feynman, Leighton, and Sands 1969, 37-1). Difficulties in the discussion of the wave-particle issue were further aggravated by disagreement about which (wave or particle) attributes are "essential" and which are merely artifacts of interaction. 12 Here ambiguity was connected with a fruitful theoretical freedom, exploited by physicists from the early days of quantum theory until today. We have already mentioned that Duane, Jordan, and other physicists did not feel compelled to consider the diffraction of light (or matter) to be an indication of its wave nature-the diffraction was merely an artifact of the quantized structure of the grating used in the experiment. Similarly, theorists who wished to avoid ascribing discontinuities to radiation (Debye and Ehrenfest-see Darrigo11986) located all the discontinuities in the interacting matter. Even localized detection of light quanta on a photographic plate, though generally held to be an unequivocal sign of their particlehood, need not be considered so-localized detection events" can be regarded as originating from the quantized energy levels of the atomic constituents of the detector" (Ghose and Home 1992,1438).13 What some quantum theorists consider today a more adequate indication of single particle-like behavior are "single photon states" of light.!' For an ideal U. From a verificationist point of view, this distinction is meaningless, yet theoretically it is difficult to abstain from discussing abstract cases. Thus Bohr often talked of the propagation of radiation in free space, which. in his opinion, must be pictured by a wave theoretical model. 13. "One observes discrete events giving rise to an interference pattem even with strongly attenuated sources of dassicallight" (Ghose and Home 1992, 1438). 14. Such "single photon states" are Fock-space states that are eigenstates of the "photon number operator," which corresponds to the eigenvalue unity (Ghose and Home 1992, 1436).

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single photon state, the probability of joint detection of more than one photon is zero-single photon states imply the notion of single particle-like behavior. IS With this definition of particlehood, Ghose and Home argue, Bohr's thesis of mutual exclusivity is contradicted: one can have experiments in which single photon states exhibit a tunneling effect (tunneling is considered exclusively a wave phenomenon). Other physicists argue the applicability of Bohr's thesis of mutual exclusivity by considering interference, rather than tunneling, as the hallmark of wavelike behavior (Scully, Englert, and Walther 1991 ).16 Oearly, the lively discussion continues. The thesis of the mutual exclusivity of waves and particles is found applicable to some situations, yet inadequate in others, depending on the definitions of the terms used. Theoretical preferences relating to the wave-particle issue are closely connected with intellectual temperament and personal research experience. Matters of taste often dictate what seems fundamental and what derivative. De Broglie, considering quantization a mystery, introduced wave-particle duality as a way to deduce and elucidate Bohr's quantized energy levels in an atom. It was a seductive project: even Bohr, despite his claim of further "irreducibility" of the "atomic postulate," initially praised the de Broglie-Schrodinger approach for its ability to decode quantization (chapter 6). Others, such as Duane, took quantization as given and constructed their views about the wave-particle issue accordingly. The ambiguity of wave and particle terminology resulted not only in theoretical freedom but in an abundance of ad hoc moves and inconsistencies. Born's case is typical. Discussing the Bohrian doctrine of complementarity, Born defended the thesis of the mutual exclusivity of waves and particles by an ad hoc extension of the definition of a particle (a discussion strangely at odds with Born's own probabilistic interpretation of quantum mechanics). Claiming that it is misleading to assert that at the detector in the two-slit experiment (in Born's case, a photoelectric cell), the corpuscular nature of light is revealed simultaneously with the wave aspects of the interference pattern, Born proposed the following definition of a particle: "To speak of a particle means nothing unless at least two points of its path are specified experimentally" (1969,101). 15. Single photon states are unique in this sense: for all other states (classical or nonclassical), "the probability of a double detection is different from zero even when the average number of photons ... is less than unity" (Ghose and Home 1992,1436). 16. These authors argue that in interference-type experiments (Bohrian two-slitexperiments, for example), the quantum formalism implies the disappearance of the interference pattern whenever one tries to obtain "which path" (particle) information. thus supporting the mutual exclusivity of waves and particles.

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It is not clear why two points are necessary for the definition of a particle, unless one intends with these two points to specify the particle's path-something forbidden by the Copenhagen version of quantum theory. Born, in fact, inconsistently talks about particle paths: "If we propose to carry out the 'demonstration of a corpuscle,' we must settle the question whether its path has gone through the upper or the lower of the two slits of the receiver" (1969, 101, my italics); or similarly: "If pure interference is to be observed, we are necessarily precluded from making an observation of any point of the path of the light quantum before it strikes the screen" (1969, 102, my italics),l7 The frequent use of the notion of the "path" of a particle, or a particle "trajectory" (pauli 1973, 14), in the discussion of such thought experiments-despite the Copenhagen claim that continuous space-time motion is incompatible with the uncertainty relations-demonstrates that such visualizable interpretations cannot be carried through without inconsistencies, just as Heisenberg and Bopp asserted. And with this realization, wave-particle complementarity, as Bohr conceived it, loses much of its power and appeal. Bohr had his own definitions of wave and particle attributes. He never accepted a complete analogy, or basic symmetry, between matter and radiation, maintaining all his life a peculiarly unshakable commitment to classical wave theory and somewhat resenting assertions of the reality of light quanta. Thus Bohr claimed that "there can be no question of replacing the wave picture of light" (1933,5) and that "interference patterns offer so thorough a test of the wave picture ... that this picture cannot be considered as hypothesis" (1933,4). When one deals with the interference picture, "light quanta with such definite entities of energy is something which of course does not come into the picture at all. It is just that wherever light energy is released into material, then it is in the quantity hv" (1937d [lecture 3], 269; see also Stachel1986, on Bohr's attitude toward light quanta, or photons). According to Bohr, "The tangible content of the idea of light quanta is limited, rather, to ... conservation of energy and momentum" (1929a, 113).18 This idea that the particle nature of radiation is essential only in 17. We see here how arbitrary is the condition of haVing "two points," for Born talks of "any point of the path." U all one needs is turo points, this condition is satisfied by the definite position of a light emitter, or electron gun, and of a slit, unless one assumes a strange transmutability in the same experimental arrangement of electrons or photons, which left the emitter as waves and passed through the slits as particles. 18. Born used this defini tion while discussing the Compton effect (rather than the previous case of a two-slit experiment): "The corpuscular description means at bottom that we carry out the measurements with the object of getting exact information about momentum and energy relations" (1969, 97).

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the interaction of radiation and matter was at the core of Bohr's idea of the mutual exclusivity of wave and particle pictures: "It is not possible in a single picture to account for the various properties of radiation. For certain properties the idea of wave propagation is quite essential. For the study of the energy and momentum transferred in the individual processes, the photon idea, close to the particle concept, is equally essential" (1957b [lecture 3],609). As I have previously argued, Bohr did not assign a realistic significance either to the wave picture of matter or to the particle picture of radiation (a point also made by Murdoch 1987, 78). These pictures, as opposed to realistic models of waves and particles in the classical realm, are needed for "visualization," for adapting oneself intuitively to a nonintuitive quantum world. This being the case, it is not clear why, and in what sense, they are "equally necessary" (Murdoch 1987, 78). Nor is it clear, one might add, why it is important that they be mutually exclusive: why should imprecise and limited analOgies be consistent with each other? . Bohr's idea of the mutual exclusiveness of waves and particles had its roots in the Como lecture. What he considered contradictory, and therefore mutually exclusive initially, were the ideas of a single, infinitely extended harmonic wave and a precisely localized, free material particle (chapter 6). Yet their contradictory natures did not bother Bohrthey were "abstractions," unrealizable in physical experimental situations. The contradiction between these two ideas, Bohr argued, is resolved by the de Broglie....:Schrodinger wave packet. As Bohr's emphasis on the usefulness of wave imagery was replaced gradually by an operational emphasis on measurement, his method of avoiding contradictions changed: moving away from the notion of a wave packet, he turned to discussions of the mutual exclusivity of experimental arrangements for disclosing wave and particle properties, respectively. Bohr adopted wave-particle complementarity by analogy with kinematic-dynamic (space-time and causality) complementarity. In the case of kinematic-dynamic complementarity, which followed in a straightforward way from Heisenberg's uncertainty relations, the mutual exclusivity of the respective experimental arrangements was demanded for the consistency of the quantum mechanical scheme. This misleading analogy between wave-particle and kinematicdynamic complementarity resulted in the widespread misconception that there must be a precise connection between the two. Not surprisingly, different commentators interpreted this connection in different terms-some correlated energy and momentum with particles, and space-time with waves (Born 1969, 97), while others identified particles with space-time. Yet the two kinds of complementarity are not reduc-

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ible to each other, as an analysis of the Como lecture shows. In the Como lecture, as I have argued, "complementarity between space-time and causality" is an umbrella concept covering several basically different physical situations. In elucidating the applicability of conservation laws in the Bothe-Geiger experiment, Bohr applied causality to particles, and space-time notions to waves. In discussing the limits of space-time models for an atom in a definite stationary state, he correlated spacetime with particle models, and causality with the notion of a wave (a definite stationary state is represented by a constant value of energy and by a single harmonic wave). The frequent assumption that one kind of complementarity reduces to the other is unfounded and leads to confusion.

Ideological and Pedagogical Uses of Wave-Particle Complementarity If Bohr's wave-particle complementarity is neither unambiguous nor necessary in theoretical research, what is its function? To what uses is it put and what aims does it serve? . Orthodox visualizable discussions of wave-particle complementarity have clear ideological and pedagogical objectives. This is the main reason quantum theorists, most notably Heisenberg and Born, sometimes supported Bohr's discussions of wave-particle complementarity in public. Their support for an accessible, Bohrian interpretation became especially strong when they targeted their expositions toward wider audiences and not only the mathematically initiated: liThe existence of this mathematical theory [quantum mechanics] shows that the whole structure is logically coherent. But this proof is rather indirect and convincing only for those who understand the mathematical formalism. It is therefore an urgent task to show directly for a number of important cases why, in spite of the use of two such different pictures as particles and waves, a contradiction can never arise" (Born 1936, 47). The status of wave-particle complementarity is closely tied to the Bohrian doctrine of the necessity of classical concepts. If one gives up this controversial, if not unfounded, doctrine, the basic role of waveparticle complementarity fades away. The necessity of classical concepts, the overthrow of the concept of reality (the impossibility of a quantum ontology), and the finality of indeterminism-all are tied to wave-particle complementarity in the overall rhetoric of the inevitability of the Copenhagen orthodoxy. Not surprisingly, those physicists who opted for some version of realism-Bohm, Schrodinger, Einstein, Lande-rejected Bohrian complementarity. Wave-particle duality is also extensively used in the rhetoric of the inevitability of indeterminism. Born's assertion is typical: "It is clear that the dualism, wave-corpuscle,

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and the indetenninateness essentially involved therein, compels us to abandon any attempt to set up a deterministic theory" (1969, 102, my italics). The philosopher Norwood Hanson (1958, 1959) followed the orthodox guidelines in arguing that wave-particle complementarity necessarily excludes a deterministic alternative to the Copenhagen interpretation (for a full discussion, see chapter 14). Wheaton opened his valuable historical description of the wave-particle issue in the early days of quantum theory by emphasizing its importance to the "overthrow" of determinism: "The first years of this century witnessed the final rejection of determinism in physical theory; there is no more compelling example of this than the synthesis forged in the early 1920s between theories of matter and theories of light" (1983,3). The most extensive use of wave-particle duality was the simple derivation and legitimation of the uncertainty relations. 19 The easiest, most accessible way to demonstrate the uncertainty relations is by identifying a particle with a limited wave field, the argument Bohr presented in the Como lecture, and consequently the way many textbooks introduce the uncertainty formula. Heisenberg, who considered the uncertainty relations fundamental to arguments for the self-consistency of quantum theory, was willing to use Bohr's accessible dualistic explanation of the uncertainty relations for wider audiences and for pedagogical purposes. As he later revealed, he used Bohr's complementarity because "it did not do any harm" to his own explanation, yet he did not believe "it was necessary" (interview with Heisenberg, AHQP). The reason wave-particle complementarity is not necessary for an elucidation of the uncertainty relations is that Heisenberg's formula follows from the mathematical formalism of Dirac-Jordan transformation theory, while wave-particle complementarity does not. As Jammer put it: "Complementarity is an extraneous interpretive addition to it [to the formalism]" (1974, 60-61). Moreover, wave-particle complementarity is always discussed for a very limited, physically uninteresting casethat of a free particle. Bohr elaborated the de Broglie-Schrodinger idea of a wave packet and the Planck-Einstein-de Broglie relations (E = hv, P = hk), which Schrodinger had used to argue the inapplicability of particle concepts in the microdomain, into an argument for waveparticle complementarity, uncertainty, and indeterminism.20 In fact, the 19. Conversely, the use of wave and particle visualization means the uncertainty formula must be taken into consideration: One can apply the wave or particle picture by taking into consideration limitations imposed by the uncertainty relation (Heisenberg 1958,43). 20. Initially, Bohr used the Planck-Einstein formula E = I,v to argue the inapplicability of particle concepts-see his Bohr-Kramers-Slater theory, in which, due to the "irrationality" of this formula, Bohr was eager to avoid the corpuscular concept of light quanta at any price.

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wave-particle duality expressed in the idea of a wave packet is not compatible with Bohr's later elaborations of complementarity, which emphasize the mutual exclusiveness of wave and particle attributes. The continuing confusion between wave-particle duality and wave-particle complementarity gives the impression that most physicists accept waveparticle complementarity, while they only endorse wave-particle duality. Born and other physicists sometimes followed Bohr in his rhetoric of the inevitability of wave-particle duality: "The lasting result of Bohr's endeavors is the simple consideration given above [analysis of the wave packet] which shows with irrefutable logic that the Planck-de Broglie laws of necessity imply the duality [of] particles-waves" (1953a, 128). As already noted, the Gottingen-Copenhagen physicists later ascribed a realistic wave meaning to a single particle (a three-dimensional wave packet) but continued to treat the "'-function for higher dimensions as an abstract, purely mathematical concept. This artificial divide between three and more dimensions has important implications. If wave-particle complementarity applies only to free particles, the concept is too limited to be of general significance and wave-particle complementarity becomes marginal, if not superfluous. If, for reasons of homogeneity and consistency, one applies the abstract probabilistic particle interpretation to a single particle as well, then the wave packet in the three-dimensional case is as "abstract" as in the multidimensional case and simply signifies the probability of a particle's having a certain position value. If one extends the basic particle substratum, guided by probabilistic lawfulness, to the case of a single particle, the whole argument for wave-particle complementarity dissolves. We do not have in this case reality of matter waves even for a single particle, viewing it instead as the three-dimensional case of the same probability calculus that is used in higher dimensions. The last stand is implied in the following remark by Feynman: "Although one may be tempted to think in terms of 'particle-waves' when dealing with one particle, it is not a good idea.... For if ~ere are two particles, the amplitude [probability] to find one at and the other at r2 is not a simple wave in 3-dimensional space, but depends on six space variables r1 and r/' (Feynman, Leighton, and Sands 1969, 3: 3-4). This point of view is indeed consistent with Born, Heisenberg, Pauli, and Jordan's particle-kinematic probabilistic interpretation. Yet, following Bohr, the orthodox physicists often invoked the three-dimensional wave packet as more than a formal analogy. Pauli, in popular presentations, used the idea of a wave packet not merely as a visualizable illustration but as a phYSical explanation for the uncertainty relations: the uncertainty relations are valid because in wave imagery no packets exist that contradict the relation axa(l/ A) - 1

'I

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(the relation between the spatial limitation of a group of superposed waves and wavelength A; Pauli 1950). If wave-particle complementarity is an arbitrary addition to quantum theory, we can easily understand why it generated so much sterile verbiage.21 Born again appears on the scene with a rhetorical sword in hand (see my previous discussion of Born's confrontation with SchrOdinger on quantum jumps), this time instigated by Lande's (1965) criticism of wave-particle complementarity. Lande argued that" duality" might sometimes be "helpful for heuristic reasons" but that it is totally "unphysical." He stressed eloquently and repeatedly that the "crucial" evidence for matter waves, supposedly impossible to explain otherwise-diffraction phenomena-is adequately explained by Duane's "third rule" of the quantization of linear momentum for a diffracting lattice, which is a body periodic in certain space directions and which therefore can change its momentum component only by discrete amounts. This condition yields a set of discrete angles of electron deflection that determine and explain the diffraction pattern without the assumption of de Broglie waves. Similar considerations can, according to Duane, explain all of the other "mysteries" that allegedly can only be accounted for by the "fiction" of the dual nature of matter (Lande 1965, 123). Lande (1965) also did not accept Heisenberg's condliatory formulation of the "symmetry," rather than the "duality," of waves and particles, based on second quantization: a photon whose role is merely that of a quantum number attached to the periodic components of the continuous Maxwell field hardly deserves to be regarded as a particle. Similarly, the fact that atomic probabilities for the distribution of particles obey a rule of wavelike interference rather than of simple (classical) addition is not a reason to conclude that particles have a "wave nature," but rather a stimulus to search for a simple and logical foundation from which such interference (or equivalent rules for matrix multiplication) for probability amplitudes can be deduced. 22 Such a simple and logical foundation, from which Lande succeeded in deducing the interference of probabilities, contains the non-quantum postulates of symmetry, order, and coherence (Lande 1955). Lande's derivation of the interference of probabilities was largely ignored by representatives of the Gottingen-Copenhagen alliance, but his attack on the Copenhagen credo was countered at once. Rosenfeld dismissed Lande's work as "making a muddle of a perfectly clear situ21. In contrast to the idea of a wave-particle synthesis, which, [ argued earlier, served as a fruitful heuristic principle. 22. The basic innovation in the traditional view in physics and philosophy, according to Lande, was not "wave-particle duality" or "reality" but the irreducible statistical lawfulness in the quantum domain.

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ation" (1956, 133). Born and Walter Biem (1968) published a highly critical rebuttal of Lande's views, using the characteristic rhetorical tactics of discrediting the opponent and appealing to authority. Lande" does not realize the historical origin of the dualistic interpretation" and does not "correctly describe its physical meaning." He is driven by "prejudice" and "dogma," and he "ignores important physical discoveries" (1968,51). Dualism is a "discovery, and not an invention" (1968, 54) of Einstein himself, made when Einstein was young and drew "irrefutable inferences" (1968,51), as opposed to Einstein's deterioration into speculation in later years. While every physicist must accept Duane's rule, which" describes correctly all experiments of momentum exchange" on periodic structures (1968, 51), the rule is "obscure" without de Broglie's idea of the connection between particles and matter waves. Besides, the dualism Lande himself introduces ("particulate nature of matter and wave nature of light") is even more unsatisfactory. And while Lande's derivation of the quantum mechanical probabilistic rules" can be interesting in itself," there is no need, Born and Biem reprimanded, to accompany it "by attacks on supposed enemies" (1968, 55). Lande's (1968) answer was a fitting rhetorical counterattack: waveparticle duality "received its death-knell" from none other than Born himself, through his "admirable" statistical interpretation of the "'function in term of particles; to present Einstein" as a champion of dualism is utterly unhistorical"; Lande's own views are no longer those "of a lonely Don," but are shared ''by many prominent phYSicists and philosophers of science" (1968,56). In the end, Born and Biem had no choice but to retreat: "Oearly, it is possible to formulate a quantum mechanics of particles avoiding all wave-like terms." Still, they asked, "Why the effort?" (1968,56).

CHAPTER 12 ~

Complementarity as Metaphor Perhaps our ability to convince others depends on the intensity with which we can persuade ourselves of the force of our own imagination. Words attributed to Niels Bohr by Heisenberg 1971, 131

We have at the end only to take recourse to painting with words just like one paints, as [an} artist paints with colors just trying to use them in such a way [as} to be able to give to one another just an impression of certain connections of certain harmonies. Niels Bohr 1937d, 354

Bohr felt that whenever one came with a definite statement about anything, one was betraying complementarity. Interview with Leon Rosenfeld, 22 July 1963, AHQP

Introduction

Bohr was an avid storyteller. A whole generation of physicists was raised on Bohr's stories. As Pais reminiscences: "Sooner or later, for the purpose of illustrating some point ... Bohr would tell one or more stories" (1991, 6). The most inspiring, never-ending story, which Bohr never tired of repeating, was about the "great interconnections" in science and life as revealed by complementarity. But what is complementarity? It is not a principle, as both Bohr and Heisenberg often stressed. Even less is complementarity a model. A model of quantum theory should contain something essentially quantum. Complementarity does not. Complementarity is a metaphor, powerful enough to cut across many domains, inspiring enough to construct a new sensibility. Complementarity is not a rigorous guide to the heart of the quantum mystery. Nor do Bohr's numerous analogies between quantum physics and other domains, such as psychology or biology, withstand close

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scrutiny. Complementarity does not reveal preexisting similarities; it generates them. 1 Complementarity builds new worlds by making new sets of associations. These worlds are spiritual and poetic, not physical. Complementarity did not result in any new physical discovery"it is merely a way to talk about the discoveries that have already been made" (interview with Dirac, AHQP). Only great poets and great prophets succeed in imposing their private associations on the whole culture. Einstein considered Bohr "a prophet," and Freud the author of a "huge mythology." Einstein had little sympathy for either. Neither Freud nor Bohr was intimidated by Einstein's criticism. In a shrewd reply to Einstein, Freud was anything but apologetic. Freud had no intention of demarcating psychoanalysis from science: "But does not every natural science lead intimately to this-a sort of mythology? Is it otherwise today with your physical science?" (quoted in Erikson 1982, 168). As is suitable for a prophet, Bohr talked in fables and parables. Offending some sensibilities, Heilbron compared Bohr to a "guru" (Heilbron 1987, 221). As gurus do, in his later years Bohr inspired by personal contact. 2 As Otto Frish recalled, "after dinner, we sat close to him-some of us literally at his feet, on the floor-so as not to miss a word" (French and Kennedy 1985, 353). Bohr had the exclusive authority to reveal the "hidden hannonies" in nature. When one did not understand Bohr, the reaction was not inquiring criticism-it was a feeling of awe for the "deep and subtle" philosophy of Bohr.3 Bohr expected the new framework of complementarity he had built to be taught to children in schools, just as the heliocentric theory is taught (interview with Bohr, AHQP). Even Bohr's close collaborator and coauthor of complementarity, Pauli, thought the "imperialism of complementarity" was going too far. Objectivity, or at least the illusion thereof, demands some intersubjective agreement. No metaphor can fonn a basis for "unambiguous communication," to use Bohr's expression. Ambiguity is a necessary part of a metaphor's suggestiveness. Strip complementarity of its imaginative, imprecise associations and not much 1. Bohr's diSciple Kalckar wrote: "The connection between Bohr's work and the whole of his personality is so close that one can almost speak of an identity. The turn he gave to the trend of modem physics and through which it received its far reaching epistemolOgical consequences, arose so directly from and harmonized in such a rare degree in his own mind, that one dares to use of him the phrase which one would otherwise reserve for the great artists: that he created a world from within" (1967, 229). 2. "Only those who knew him personally could experience the immense inspiration exuding from his intuitive grasp of physics and his humane personality" (Pais 1991, 29). 3. Using the expression" deep and subtle" has become almost obligatory when writing about Bohr.

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will remain except a fancy formulation of the uncertainty principle. Bohr certainly intended complementarity to mean more than that. The ambiguity, opaqueness, and obscurity of Bohr's writings is legendary. Bohr himself, despite the heavy rhetoric of "unambiguity of communication" that underlay the inevitability of complementarity, considered obscurity a virtue. 4 Bohr's ambiguity was enveloped, by Bohr and others, in a fog of profundity. "Deep truth" cannot be adequately expressed. It is almost as hard to write about complementarity as "about religion ... being almost as long as life itself" (quoted in Blaedel 1988, 27). Presenting complementarity to a French audience, Bohr announced that "the situation is very difficult to express in words of any language" (notes for talk given at the lnstitut d'Henri Poincare, 18 January 1937, AHQP). Bohr extended complementarity to psychology, biology, and the theory of culture. In this he followed his teacher Harald Heffding, who perceived many analogies between physics and psychology (Faye 1991). Bohr elaborated Heffding's ideas, construing analogies between "disturbance" in introspection and in physical interaction. Initially, this was no more than a hunch-Bohr spoke heSitantly of "suggestive analogy" (1929b, 100), or of "more or less fitting analogies" (101). In a letter to Heffding, Bohr revealed that he had "the vague idea that there might be a possibility of proving a similar complementary relation between those aspects of the description of the individual psychological processes which relate to the emotions and those which relate to the will as that which quantum theory has shown to obtain, with respect to elementary processes in physics" (Bohr to H0ffding, 1 August 1928, quoted in Faye 1991, 58-59, my italics). Many of Bohr's analogies did not undergo any substantive change over the years. Rather, what was suggestive and vague became, merely by virtue of repetition, rigorous and compelling: "It is not a question of weak parallels. It is a question of investigating as accurately as we can the conditions for the use of our words" (Bohr 1958e, 704). When Bohr first explored the similarities between physics and psychology, he felt that we "can hardly escape the conviction that we have acquired a means of elucidating general philosophical problems" (1929b, 101). It is this conviction that sustained repetition without substantive elaboration. The initially novel and fresh metaphors became familiar, obvious. "Vague" analogies become "beautiful examples," "striking analogies" (Bohr 1958e, 704). According to Heisenberg, Bohr was a "natural philosopher," not "a 4. Bohr especially liked a fable about the talk by a rabbi that was understood neither by his listeners nor by the rabbi himself (Pais 1991).

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mathematical physicist." For a mathematical physicist, to understand or explain means to construct a suitable set of models and to specify the rules for connecting the abstract theoretical entities with empirical data. Mathematical physicists explicate the meaning of operators, eigenfunctions, observables, projections in Hilbert spaces. Bohr had no use for any of these notions. For Bohr, as for a pre-Newtonian natural philosopher, "any explanation or analysis only means to use analogies from simple experience" (Bohr 1937d [lecture 6], 353). Vico's description of what is distinctive about proper philosophizing fits Bohr especially well: "Specifically philosophic quality ... [is the] capacity to perceive analogies existing between matters lying far apart. ... It is this capacity which constitutes the source and principle of all ingenious, acute and brilliant forms of expression" (quoted in McMullin 1991, 57). Bohr was a philosopher of "harmonies," of symbolic meanings. As Pauli did not fail to notice, Bohr's correspondence between macro and micro, based on an analogy between a planetary system and a microscopic atom, retained the original medieval notion of harmonies between macrocosm and microcosm. Yet, if the correspondence principle, by an ingenious mathematical elaboration, especially in the hands of Kramers and Heisenberg, led to the new quantum theory, complementarity never left" common language." By not leaving common language, Bohr could not even attempt to construct a quantum ontology. Bohr and his followers presented this idiosyncratic choice as a prohibition in principle. Not surprisingly, many of Bohr's thought experiments intended to demonstrate complementarity contain nothing quantum in their analysis (Beller and Fine 1994). If there is a single idea that inspires Bohr's analogies, it is the breakdown of the classical concept of motion, and the loss of continuity (infinite divisibility) and of the visualizability (Anschaulichkeit) associated with it. It is this idea that inspired, often mistakenly, Bohr's intuitive discussion of the interconnection between reality, acausality, and loss of visualizability in the quantum domain. 1his idea also inspired Bohr to see a general epistemological similarity between atomic physics and psychology: "We may say that the trend of modem psychology can be characterized as a reaction against the attempt at analyzing psychical experience into elements which can be associated in the same way as are the results of measurements in classical physics" (1938b, 27}.1he loss of visualizability in physics inspired many of Bohr's far-fetched analogies: "emotions and volitions" are similar to the quantum of action because they are incapable of being represented by visualizable pictures. Improvising on the complementarity theme, Bohr gave free rein to his imagination. Many of his analogies-for example, between the quantum of action and the concept of life, between the flow of thinking and the wave

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nature of matter, or between the unity of personality and the individuality of material particles-contain no more objective content than the correspondence between dreams and winning lottery numbers outlined in an essay by his grandfather.s Many of Bohr's analogies that initially seem appealing fall apart when probed more closely. In his early writings, Bohr often draws a parallel between atomic measurement and introspection. In both cases, apparently, it is inherently impossible to separate the observing from the observed. Bohr's conclusion was that atomic interaction is in principle "unanalyzable" and "unsurveyable"-a prohibition not many working theoretical physicists would choose to comply with. Many of Bohr's examples of mutual exclusivity are far from convincing. The often repeated example of complementarity between "thoughts" and "feelings" is contradicted by contemporary psychological research (see L~zarus, Kanner, and Folkman 1980 on the connection between emotion and cognition). The mutual exclusivity of reason (associated with the masculine) and emotions (associated with the feminine) has also been subjected to penetrating critique, by feminist scholarship. Though some of Bohr's associations remain private and inexplicable, others, such as the preceding example, resonated within the culture of his time. Heisenberg, who joined Bohr in the dissemination of his metaphors, understood well their persuasive power. Though to his colleagues Heisenberg preferred to talk in unambiguous mathematical language, he appealed to the general "mental climate" when lecturing to popular audiences. 6 Bohr's numerous "harmonies" were those "useful (sinnvoll) interrelations 'belonging together' within the human mind" (Heisenberg 1979, 68).7 Bohr's writings on complementarity are metaphorical in a strong sense. Complementarity is an "artificial word," which "serves only briefly to remind us of the epistemological situation" in quantum physics (1937c, 293). Because the situation is unprecedented, one can only tum to "quite other branches of science, such as psychology or ... to thinkers like Buddha and Lao Tse" (1937b, 20). But these disciplines are themselves ambiguous and in need of more rigorous explication, so one has to tum back to quantum phYSiCS, where matters can be explicated, so Bohr intimated, more precisely. Oearly, this state of affairs cannot be understood by any "substitutive view" of metaphor, in which the literal 5. Pais described Bohr's grandfather's "witty essay" in which "the dream table establishes a correspondence between a specific type of dream and the lottery number to be picked" (1991, 35). 6. "Every scientific theory arises in a certain mental climate ... the author of the theory may be only vaguely conscious of it" (Heisenberg 1979, 65-66). 7. I would translate 5i7l1l001/ as "meaningful:' rather than "useful."

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meaning of the primary subject can replace the metaphorical meaning of the secondary one. Even the "interactive" view of Max Black (1962) is only of limited help. According to this view the primary and secondary domains (for example, physics and psychology) interact so as to produce novel understandings of both, but Black assumes that the primary domain is understood to a considerable degree. No such wellunderstood primary domain exists in Bohr's analogies. Rather, we encounter here a hermeneutical circle. Bohr's complementarity should be approached as a foreign culture, as a newly encountered, unfamiliar symbolic world. Clifford Geertz's characterization of the anthropological approach is a fitting one to describe the encounter with the strange framework of complementarity: "Hopping back and forth between the whole conceived through the parts which actualize it and the parts conceived through the whole which motivates them, we seek to tum them by a sort of intellectual perpetual motion into explications of one another" (1976, 236). In this hermeneutical web of metaphors, "hopping back and forth" often interchanges what is foundational and what is derivative, explanandum and explanans. As I will shortly argue, Bohr's language of "correspondences," conjoining certain concepts and thus creating "harmonies," was inspired by powerful, though often misleading, images. His understanding was that of a poet, a mystic, an artist-Bohr's own words (this chapter's epigraph) characterize his thought especially well: "We have at the end only to take recourse to painting with words just like one paints, as [an] artist paints with colors just trying to use them in such as way [as] to be able to give one another just an impression of certain connections of certain harmonies" (1937d, 354). The Web of Correspondences and Harmonies Bohr's thought teems with "correspondences" and "harmonies." If, in the old quantum theory, such correspondences served as powerful heuristics (Jammer 1966; DarrigoI1992a), after 1927 Bohr advanced the idea of correspondences, or harmonies, to legitimate an unfamiliar and abstract quantum theory. The idea of harmony between the possibilities of observation and theoretical definition pervades, as I have argued, the Como lecture. Later, when Bohr elaborated the lessons of complementarity, he argued that features of the quantum formalism "correspond" to the freedom to choose the appropriate measuring devices. 8 Similarly, 8. "The possibility of disposing of the parameters defining the quantum mechanical problem just corresponds to our freedom of constructing and handling the measuring apparatus, which in tum means the freedom to choose between the different complementary types of phenomena" (Bohr 1948, 452).

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"emphasis on permanent recording under well-defined experimental conditions ... corresponds to the presupposition, implicit in the classical physical account, that every step of the causal sequence of events in principle allows of verification" (my italics). It is this "correspondence" that allows one to view quantum mechanics as fulfilling" all demands on rational explanation with respect to consistency and completeness" (Bohr 195&, 6). By presenting numerous "correspondences" between the fonnalism and the "conditions of experience," Bohr created the illusion that the quantum fonnalism is a direct confirming instance of complementarity, thus enforcing the acceptance of an unfamiliar formalism and a new philosophy of physics concurrently. Heisenberg, when presenting the lessons of quantum theory to wider audiences, sometimes adopted Bohr's language of correspondences. Arguing that the quantum formalism represents our knowledge rather than the objective course of events, Heisenberg pointed out the correlation, or reciprocal "image," between the act of registration in observation and the collapse of the wave function: "The discontinuous change in the probability function, however, takes place with the act of registration, because it is the discontinuous change in our knowledge in the instant of registration that has its image in the discontinuous change in the probability function" (1958, 54, my italics). Earlier, Born had advanced his statistical interpretation of the wave function and his statistical solution of the collision problem also by asserting a preestablished harmony between the possibilities of theorizing and the possibilities of experimentation (Beller 1990). Bohr's writings are permeated not only with hannonies between theoretical advances and experimental possibilities but with what he considered necessary connections between key concepts, such as causality, visualizability, objectivity, and the distinction between subject and object. These connections, firmly entrenched in Kantian philosophy and in the classical idea of motion, Bohr fully embraced. His philosophy of complementarity, as I have argued, sprang from his basic intuition of the breakdown of the classical idea of motion (overthrow of visualization, causality, and reality) and was aided initially by the incorrect idea of disturbance (the impossibility of demarcating object from subject, the inseparability of phenomena and their means of observation, and the subsequent "indivisibility," or "wholeness," of the quantum interaction; chapter 7). In the classical idea of motion, spacetime concepts, conservation laws, and visua1izability (Anschaulichkeit) are intimately connected: from given initial space-time conditions and the conservation laws (causality), one can calculate the subsequent dynamical evolution of a system, as well as fonn a model (a picture, a visualization) of its behavior in space-time. Bohr's initial conflation of

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the ideas of causality and reality, and of causality and visualization, had its source in the classical idea of motion-Bohr thought intuitively that the breakdown of the classical idea of particle motion implied the breakdown of both causality and our concept of reality.9 Bohr characterized classical description as "causal pictorial" (1960c, 11), and he retained this intuitive, yet incorrect, idea of a necessary connection between causality and visualizability 10 throughout his life, even as his ideas about reality and acausality changed (chapter 7). If visualizable classical physics is "causal," then it is natural that the nonvisualizable quantum physics be noncausal: "In conformity with the non-pictorial character of the formalism, its physical interpretation finds expression in laws of essentially statistical type" (Bohr 1958c, 3, my italics). Bohr's metaphorical framework of harmonies and correspondences is sustained by such expressions as "finds logical expression," "is suited," "it is not surprising that." Consider two characteristic examples: "Since, ... we cannot neglect the interaction between the object and the instrument of observation . . . , it is not surprising that in all rational applications of the quantum theory, we have been concerned .with essentially statistical problems" (Bohr 1929b, 93, my italics). And many years later: "We are dealing [in quantum mechanics] with a mathematical generalization of classical physical theories which by its nonpictorial character is suited to embrace the indivisibility of quantum phenomena" (Bohr 1957a, 669, my italics). The two examples sound innocently similar. Yet they are worlds apart. The first is taken from Bohr's early writings at the time when all of his considerations were informed by the idea of disturbance. It is with the help of this idea that Bohr justified the connection between the indivisibility of measurement interaction and the necessary overthrow of causality and reality (chapters 7 and 9). As Bohr himself later repudiated the misleading idea of disturbance, no intuitive ground remained for his analysis of the inevitability of indeterminism and the overthrow of objectivity in the quantum domain. Before 1935, the idea of disturbance provided the illusion that Bohr's argument was grounded in a.. solid, experimental state of affairs. No illusion of this sort could be retained when the idea of disturbance was discarded and Bohr declared that quantum theory was merely a tool for the description and prediction of measurement results. In the post-1935 framework Bohr had to 9. Supplemented by his doctrine of the indispensability of classical concepts. this intuition led Bohr to deny the possibility of an objective causal theory, such as Bohm's. 10. One can have a nonvisualizable deterministic description, as well as a visualizable nondeterministic description.

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postulate, rather than explain, the inseparability between measuring and measured, as well as the indivisibility, or wholeness, of quantum phenomena. l1 Bohr's wholeness often meant nothing more than an operational definition, where the meaning of a concept is intrinsically tied to the procedure of measurement. How is then the "nonpictorial" character of quantum physics suited to embrace the indivisibility of quantum phenomena? If the phenomena are defined relationally, or contextually, there is little reason for discarding causality a priori. Not surprisingly, in Bohm's version of quantum mechanics wholeness does not lead to acausality. In fact, Bohr retained the intuition of a correspondence between wholeness and acausality from his older, discredited framework of disturbance. Thus Bohr's complementarity is built on a clustering of associations, which are nowhere grounded. Bohr's liberal interchanging of explanandum and explanans leads to his peculiar assertion that Heisenberg's uncertainty relation follows from complementarity: "The ultimate reason that in no conceivable measurement conjugate quantities can be fixed with a greater accuracy than that given by (5) [the uncertainty formulas] is indeed the complementary character of the pictures employed" (1939,391). Complementarity, begot by repetition, assumes a life of its own and begins to serve as a basic explanatory concept, from which other aspects of the Copenhagen philosophy seem "inevitably" to follow. When he was in a Copenhagen mood, Heisenberg too freely interchanged explanandum and explmums. He often argued, using disturbance imagery, that the atomic constitution of matter leads to the uncontrollability of the measurement interaction. Yet sometimes his reasoning was reversed-it is the uncontrollability of the interaction that necessitates the finite divisibility of matter: "The existence of elementary particles is only justified by this fact [uncontrollability of interaction]" (1952, 73). The Copenhagen framework is built on "correspondences" and "har_ monies" among a cluster of intuitively interrelated ideas, despite the fact that the meaning of these ideas and the nature of their interrelation vary over time. It is this clustering that misled Bohr's readers into regarding his conceptual framework as basically stable. Because his reasoning is essentially metaphOrical, Bohr often uses such expressions as "harmonizes," "corresponds," "is suited to," or "finds proper expression," rather than "follows from" or "is deducible from." Here lies a 11. One could, of course, tum to the quantum formalism and fully acknowledge its new features of nonseparability and nonlocality. Yet Bohr, who refused or was unable (see the discussion of Bohr's attitude toward mathematics below) to leave the "common language," avoided this option altogether.

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striking difference between the analogical use of the correspondence principle and the metaphorical use of complementarity. The correspondence principle guided physicists, by suitable analogies, to explore the new quantum realm in ways suggested by regularities existing in the well-explored (primary) classical domain. No such primary domain exists in the complementarity framework. The complementarity principle was a metaphOrical tool of legitimation-it led to no new physical knowledge. "Wholeness" as Metaphor "Hunger for wholeness" permeated the early twentieth century's Weimar culture (Gay 1968, 70-101). This hunger was not confined to the Weimar republic. In Denmark many intellectuals inherited the craving for "wholeness," "unity," "irrationality," and "unanalyzability" from Kierkegaard's existential philosophy. The young Bohr admired Kierkegaard (see Holton 1970 and Jammer 1966 on Kierkegaard's impact on Bohr). The wholeness, interconnectedness, and unity of science was, albeit from a different angle, a central concept in Kantian philosophy, which, as a result of the "back to Kant" movement, dominated academic philosophy in German-speaking countries. 12 From his neo-Kantian teacher and friend Harald H0ffding, Bohr learned that "true knowledge does not consist of accumulated experiences but is insight into the interrelationships between experiences" (Faye 1991, 9). In a Kierkegaardian vein, H0ffding attempted to create "unity and harmony of the opposing views" (Faye 1991, 12) and a holistic notion of science that integrates physics and psychology. Bohr's early analogies between quantum physics and psychology, and his general notion of wholeness, are due to H0ffding. It is from H0ffding, according to Bohr's own words, that he learned about the "relativity of all our concepts" (1932,200,203). H0ffding's impact was one of those meaningful mental processes that cannot, according to Bohr, be fully explained or analyzed: H0ffding's "influence and guidance could be absorbed almost without being felt by the one who received it" (1931a, 178). It was because of H0ffding's discussions about the "balance between analysis and synthesis" that Bohr maintained throughout his life the centrality of the idea of" wholeness": "While the whole may be built of individual parts, the appearance of each individual part is influenced in tum by the whole." H0ffding's discussions had for Bohr and "for many of the listeners at his lectures as well as the even more numerous 12. See Beller (forthcoming) for Kant's impact on Einstein's philosophy and Chevalley (1994) for an analysiS of the Kantian context of the Bohrian use of the terms Al1schauullg and "symbol." Bohr's usage of "wholeness" also belongs to this context.

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readers of his book, a significance much deeper than what anyone of us could easily explain" (Bohr 1931a, 177). Heffding's general idea of wholeness permeated Bohr's writings on complementarity from his Como lecture until the end of his life. Like the terms "complementarity" and "causality," the word "wholeness" in Bohr's writings has many different meanings and is exemplified by different analogies in different contexts. Some of these analogies conflict with each other, while others are misleading (see the discussion below). None of these analogies adequately reflects the post-Bell notions of "inseparability" and "nonloca1ity." In what follows I will discuss several of Bohr's metaphorical uses of the idea of wholeness. In these discussions Bohr constructed an illusion of explanation, by using outmoded traditional (classical) principles and ideas. Bohr's early intuition of wholeness drew strength from his misleading notion of disturbance. Wholeness, based on finitude and atomicity, is expressed, according to Bohr, by the prototype of the quantum jump_If an individual process, incapable of more detailed description, by which the atom goes over from one so-called stationary state to another" (1929a, 108). As Bohr later argued, the essential characteristic of the quantum interaction is its uncontrollability, not its finitude. I have argued that the uncontrollability follows from the mathematical formalism of quantum mechanics (chapter 9)-it cannot be deduced from a general philosophical principle. In Bohr's pre-1935 writing, "uncontrollability" figures in his discussions of the uncertainty principle-uncontrollability prevents a circumvention of uncertainty. While Bohr avoided discussing the mathematics of quantum mechanics, he appealed to the age-old metaphor of "hiding" and elusive Nature, who prevents the inquirer from getting too close to her and "penetrating" her secrets. Thus, Bohr argued, we cannot know the position of particles in an atom in a given stationary state, because the use of measuring instruments will imply "an exchange of energy between the atom and the instruments which completely hide the energy balance" (1932, 201, my italics). This idea drew its metaphOrical strength from an analogy with biology: "In every experiment on living organisms there must remain some uncertainty as regards the physical conditions to which they are subjected, and the idea suggests itself that the minimal freedom we must allow the organism will be just large enough to permit it, so to say, to hide its ultimate secrets from us" (Bohr 1933, 9, my italics). Initially, disturbance (we erase phenomena while trying to observe them) was the metaphorical tool used to express wholeness-nature hides its detailed working by our interference, though no knowledge without such interference is possible. Later, Bohr distanced himself

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from the disturbance notion and introduced a "distinction in principle between the objects we want to examine, and the measuring instruments" (1935b, 218).13 Yet the idea of disturbance, though he later criticized it, remained his most vivid, most potent metaphorical tool for discussing quantum uncertainty and wholeness without recourse to mathematical formulas. This is the reason Bohr and Heisenberg, while denying its viability at times, regressed into using the idea of disturbance. 14 Even when he rejected the notion explicitly, Bohr implicitly retained the intuition of disturbance and of its "hiding" aspect in his later (especially post-1935) discussions of individuality or wholeness. This intuition is apparent in Bohr's notes for a talk he gave at the Institut d'Henri Poincare in Paris in 1937: "Individual phenomena in quite a new sense in physics. When trying to analyze, phenomena disappear. They appear only under conditions where it is impossible to follow their course" (18 January 1937, AHQP). The example that Bohr provided was the two-slit experiment-if we could determine, by momentum transfer, through which slit the particles had passed, we would necessarily have "latitude" in the position of the measuring diaphragm and would thus exclude the appearance of an interference effect. This argument is repeated in an obscure manner in the Hitchcock lectures (Bohr 1937d, 323) and is much more lucidly elaborated in "Discussion with Einstein" (Bohr 1949, 217). Bohr claimed that we cannot say what is going on with a particle between its passage through a slit and its arrival at a detectorimeasurement does not allow it because under measurement the "phenomenon ... disappears entirely" (1937d, 323).15 This reasoning makes sense in an antirealist approach, where it is meaningless to discuss behavior and properties independently of measurement-here "analyze" means "to measure": "we actually cannot at all analyze in such an arrangement ... what is going on from the time the particle comes in until it is caught. We cannot control that without wiping the phenomenon out entirely. The phenomenon is in that sense an individual phenomenon, just like the individual process of transitions between the states of the atom" (Bohr 1937d, 324). 13. Note how different the idea of "irrational," "hiding" Nature is from Einstein's argument for the comprehensibility of nature: his belief that the "subtle, but not malicious" God would not construct a world that fundamentally hides part of its workings. 14. "The electron has been pushed by the light quantum, it has changed its momentum and its velocity, and one can show that the uncertainty of this change is just big enough to guarantee the Validity of the uncertainty relations (Heisenberg 1958, 47-48, my italics). 15. The problem is not that the "phenomenon disappears" but that the laws of quantum mechanics do not allow one to obtain the specifics of the previous situation by calculation. Again arguments for consistency are presented as arguments for "inevitability."

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Bohr's conception of wholeness as eradicating phenomena if we try to probe into them in more detail goes back to William James's analysis of mental phenomena. Bohr himself connected this idea with the idea of wholeness expressed by James: "If you have some things ... they are so connected that if you try to separate them from each other, it just has nothing to do with the actual situation" (quoted in Faye 1991, xvii). According to Weizsacker, "in the winter of 1931-1932 Bohr was constantly reading James" (1985, 186). Yet this Jamesian idea of wholeness is poorly suited to a characterization of quantum entanglement or inseparability. Bohr's and James's understanding of wholeness better fits the idea of a chemical compound: if we separate its constituent parts (we can do it), the phenomenon-the compound-disappears. A chemical compound is radically different from its constituting elements-water is different from hydrogen and oxygen. Such was the understanding of wholeness by Vygotsky, who argued for a holistic approach to thought and language. 16 Jamesian and Bohrian wholeness, while it may capture the idea of a classical interaction, is unable to provide insight into a quantum wholeness that evades classical analogies. Bohr's wholeness plays an essential role in his metaphorical web of seemingly interconnected ideas. Intuitively, but wrongly, Bohr argued for a necessary connection between wholeness and complementarity (the impossibility of a unified ontology) and between wholeness and indeterminism. Thus, in "Mathematics and Natural Philosophy," Bohr stated: "The essential indivisibility of proper quantum phenomena finds logical expression in the circumstance that any attempt at a well defined subdivision would require a change in the experimental arrangement that precludes the appearance of the phenomenon itself. Under these conditions, it is not surprising [again we meet the language of correspondences] that phenomena observed with different experimental arrangements appear to be contradictory when it is attempted to combine them in a single picture. Such phenomena may appropriately be termed complementary" (1956, 559, my italics). And on the existence of a "natural" connection between wholeness and determinism Bohr wrote: "The indivisibility of quantum phenomena finds its consequent expression [!] in the circumstance that every definable subdivision would require a change in the experimental arrangement. ... Thus, the very 16. "Two essentially different modes of analysis are possible in the study of psychdinger, SO, 238; and space-time, 100; and stationary states, 131; statistical, 78, 113; and time-energy, 85; and transformation theory, 86; and uncontrollability, 253; and visualization, 109; and wave-particle duality, 238. See also Disturbance; Heisenberg, Werner Underdetermination, 309 Unobservable quantities, 20 Unobservables. See Positivism Van Fraassen, B. C, 107, 176n.7, 319n.12 Van Vleck, John, 29 Virtual fields, 125 Virtual interlocutors, 7 Virtual oscillator model, 19n.4, 23, 24, 53, 132,133, 174n.4 Visualization. 30, 177; and Bohr, 236; and causality, 216, 250; and correspondences, 249-50; and Hanson, 295; and Heisenberg, 21, 69-70, 112; and intuition, 180; and quantum jumps. 215; and Schrodinger, 161; and space-time, 124. 215; and uncertainty formula, 109; and wave-packet, 124; of waves, 130. See also Oassical physics; Intuition Von Neumann, John, 18n.3, 213, 261, 275n.lO. See also Hidden variables Von Weizsacker, Carl Friedrich, 119. 204, 274-75 Vygotsky, L., 255 Wave mechanics: and Bohr,35. 122-24, 132, 171,235-41;andBorn. 186; and conservation, 133, 134; diagonality of,

Index 88; and Fichte, 58; kinematics, 23; and matrix mechanics, 32, 44; and matrix theory, 3; and Pauli, 35; positivist, 75; probabilistic interpretation of, 39-49; probability, 35; and quantum jumps, 47; received story of, 3; and Schcodinger, 6, 26,34,47,48, 127; stationary state, 26; and stationary states, 26, 34, 47, 48, 127; victory of, 36; and visualization, 124; wave ontology, 277-78; wave packets, 70,123-24,277-78. See also Wave-particle duality Wave-particle duality, 120, 189; and Bohr, 235-41; and classical concepts, 237; and complementarity, 6, 11, 12, 120, 189, 223-41; and determinism, 238; dilemma for experiments, 228; as foundational myth, 227-32; and GOttingen-Copenhagen physicists, 239-41; and Heisenberg, 225-27; myth of equivalence, 18n.3; paradox of, 225-27; and quantization. 232; and quantum electrodynamics, 232; space-time description, 127; and uncertainty, 238; visualization of, 130. See also Schrodinger, Erwin; specific concepts, issues

365

Weinberg, Steven,S Wentzel, Gregor, 28, 29, 49 Wertheimer, M., 105 Wessels, Linda, 45, 304 Westman. Robert, 291, 301, 303 Weyl, Hermann. 30, 296 Whiggish history, 211, 221 Wholeness, 13, 252-59; and Bohm, 256; and complementarity, 255-56; and disturbance, 253-54; and entanglement, 257-58; holism, 13; and indeterminism, 255; and Pauli, 256-57; of quantum phenomena, 163-64; whole numbers, 20n.5 Wien, Wilhelm, 37,186 Wilson experiments, 20, 93 Winners, narrative of, 11 Wise, N. J., 58 Wittgenstein, Ludwig, 293 Young, Thomas, 229

Zeeman effect, 29, 53 Zeitgeist, 313 Zeno's paradoxes, 207 Zemike, Frits, 92, 95-96